Dead-beat predictive current control method for high-speed permanent magnet synchronous motor under low switching frequency and fundamental frequency ratio

Abstract

The invention discloses a dead-beat predictive current control method for a high-speed permanent magnet synchronous motor under the low switching frequency and fundamental frequency ratio. Firstly, a reference stator flux linkage vector at the k + 1 moment is predicted according to reference d-q axis current and a current-flux linkage discretization model, and then the stator current at the k + 1 moment under a synchronous rotating coordinate system is predicted based on the current-flux linkage model and the predicted stator flux linkage at the k + 1 moment. And on the basis of the assumption that the current remains unchanged in a short time step length, predicting a reference stator flux linkage vector at the moment k + 2 under the alpha-beta axis, and calculating a reference voltage at the moment k + 1 according to a current-flux linkage discretization model in combination with the stator flux linkage and the stator current at the moment k + 1. Influences of sampling delay and rotor motion are considered, excellent dead-beat control of high-speed d-q axis current can be achieved even under the condition of very low SFR, d-q axis cross coupling can be almost eliminated in the high-speed transient process, and stable operation under the high rotating speed of the motor can be achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of motor drive control, and in particular to a deadbeat predictive current control method for a high-speed permanent magnet synchronous motor under a low switching frequency to fundamental frequency ratio. Background Art

[0002] With the increasing global energy consumption and the urgent need for clean energy development, how to ensure green development and improve energy supply efficiency is an important issue that needs to be solved today. Permanent Magnet Synchronous Motor (PMSM) has the advantages of high power density, high efficiency, and small size due to its use of high-performance rare earth permanent magnet materials. It is widely used in industrial fields such as aerospace and new energy electric vehicles. The simplification of its system structure and the improvement of its control strategy have been research hotspots in recent years.

[0003] Considering the switching frequency limitation of semiconductor devices, the high-speed PMSM drive has a very low switching-to-fundamental frequency ratio (SFR). In the traditional field-oriented control (FOC), space vector modulation (SVPWM) has superior dynamic response and high voltage utilization. Its sampling / control period T s Usually set to be consistent with or half of the switching period, the digital controller delay includes a step processing delay and a PWM delay, because the stator voltage or PWM signal can only be updated at the beginning of each step and requires a step to complete. For high-speed PMSM with low SFR, the control delay may be very large, which will cause oscillation or even instability of the drive system. To improve the high-speed PMSM drive under FOC, the control delay is modeled as a time constant of 1.5T s, and corresponding compensation is performed according to the complex vector transfer function. However, most of the studies to solve this problem are based on a more accurate zero-order hold inverter model, where the inverter output voltage in the stationary coordinate system is assumed to be constant over the time step. Based on this inverter model, the control delay is actually caused by the rotor movement during control, and the resulting phase delay and amplitude distortion of the stator voltage vector can be analytically derived and compensated. This delay compensation method can effectively expand the operating speed range of the permanent magnet synchronous motor and improve its control performance at high speeds; when the SFR is small enough, even with delay compensation and accurate machine parameters, the high-speed drive may lose stability. To solve the high-speed instability, a solution of complex vector current regulator and one-step prediction active damping is adopted to stabilize the FOC at a very low SFR; at the same time, the analysis in the Z domain shows that the current control of directly synthesizing the discrete current regulator is the best among various current regulator designs under FOC and can achieve stable control at a very low SFR. Although stable control can be achieved by properly designing the FOC current controller, the available control bandwidth will decrease as the SFR decreases.

[0004] Deadbeat Predictive Current Control (DBPCC) has the advantages of fast dynamic response, the ability to reduce current harmonics at a constant switching frequency, and the combination of SVPWM, which is more conducive to the high-bandwidth control of high-speed motors. Traditional DBPCC is usually based on the discretized model under the d-q axis, including two steps: one-step current prediction and stator voltage calculation. Through one-step current prediction and coordinate transformation, the one-beat inherent delay of digital control can be compensated, and the rotor movement delay can be compensated. However, through derivation, it can be known that both traditional DBPCC with and without rotor movement compensation have an average d-q axis voltage error. Although a rotor movement compensation scheme is adopted, for relatively large rotor movements, large voltage errors will still occur at high speeds. In high-speed permanent magnet synchronous motors, due to the small number of series turns in the phase windings, its synchronous inductance is usually low. Therefore, a small average voltage error will ultimately lead to a large current control error, deteriorating both the transient and steady-state control performances. Therefore, solving the problem of the decline in control performance of traditional DBPCC at high speeds is of great significance for realizing a high-performance, high-dynamic-response high-speed PMSM system. Summary of the Invention

[0005] In view of the deficiencies in the prior art, the present invention provides a PMSM voltage model based on a stationary coordinate system, enabling the method of synthesizing a reference voltage vector in the stationary coordinate system. This algorithm precisely considers the processing delay and rotor motion effects in a high-speed permanent magnet synchronous motor drive system. The controller achieves deadbeat control of the d-q axis current within two time steps, without cross-coupling across the entire speed and SFR range, and realizes the stable operation of the control system at lower SFRs.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] In a first aspect, the present invention proposes a method of a PMSM voltage model based on a stationary coordinate system, enabling the synthesis of a reference voltage vector in the stationary coordinate system. The method includes the following steps:

[0008] S1: Based on the reference d-q axis current, the current-flux linkage model of the permanent magnet synchronous motor, and coordinate transformation, predict the reference stator flux linkage vector at the (k + 1)th moment based on the integration of the reference stator voltage vector at the kth step.

[0009] S2: Based on the current-flux linkage model of the permanent magnet synchronous motor and the stator flux linkage at the (k + 1)th moment predicted in S1, predict the stator current at the (k + 1)th moment in the synchronous rotating coordinate system.

[0010] S3: Based on the assumption that the current remains unchanged over a short time step, predict the reference stator flux linkage vector at the (k + 2)th moment in the α-β axis. Calculate the reference voltage at the (k + 1)th moment according to the discretized current-flux linkage equation and the stator flux linkage and stator current at the (k + 1)th moment in S1 and S2.

[0011] Further, in step S1, the scheme for predicting the reference stator flux linkage vector at the (k + 1)th moment:

[0012] Predicting the reference stator flux linkage vector at the (k + 1)th moment includes the following steps:

[0013] The proposed method also includes two steps, one-step prediction of the stator flux linkage and current, and synthesis of the reference voltage for deadbeat control, all of which are established based on the mathematical model in the stationary coordinate system. The current-flux linkage model in the stationary coordinate system is as follows:

[0014]

[0015] To simplify the analysis, a surface-mounted permanent magnet synchronous motor is adopted, where the d-axis inductance is equal to the q-axis inductance, i.e., L s =L d =L q , and the current-flux linkage model in the synchronous rotating coordinate system is as follows:

[0016]

[0017] Ignoring the non-linearity of the inverter, the integral of the stator voltage over time can be assumed to be the product of the reference stator voltage and the time step. Therefore, using the forward Euler approximation, it can be discretized in the stationary coordinate system as:

[0018]

[0019] According to the principle of SVPWM, the present invention gives an accurate estimate of the voltage integral amount and is independent of the rotor motion. The discretization error is only determined by the estimation error of the resistive voltage drop and can be ignored at high speeds. The stator flux linkage at time k in the stationary coordinate system can be obtained from the stator flux linkage at time k in the synchronous rotating coordinate system through the inverse Park coordinate transformation, and combining with the discretized flux linkage equation, the stator flux linkage at time k + 1 can be obtained:

[0020]

[0021] where T s is the switching period time, R is the stator resistance, L s is the synchronous inductance, ψ m is the permanent magnet flux linkage, i d (k) and i q (k) are the measured values of the d-q axis currents, θ e (k) is the feedback value of the motor rotor position, i α (k) and i β (k) are the measured values of the αβ axis currents, u α (k)* and u β (k)* are the reference values of the synthesized stator voltage, ψ α (k+1) and ψ β (k+1) are the predicted stator flux linkages at the next moment.

[0022] Furthermore, in step S2, based on the current-flux linkage model of the permanent magnet synchronous motor and the stator flux linkage at time k + 1 predicted in S1, the stator current scheme at time k + 1 in the stationary coordinate system is predicted:

[0023] Steps for predicting the stator current at time k + 1:

[0024] Since the mechanical time constant is relatively large compared to the control time step, the motor speed can be regarded as constant. Therefore, the rotor position at time k + 1 can be easily calculated as θ e (k) + ω e T s, the current-flux linkage model in the synchronous rotating coordinate system is rewritten as:

[0025]

[0026] Combining the above formula, the stator current at the k+1 moment in the synchronous rotating coordinate system is obtained by performing Park coordinate transformation on the flux linkage:

[0027]

[0028] where i d (k+1) and i q (k+1) are the predicted values of the d-q axis currents at the next moment. Thus, one-step flux linkage and one-step current prediction are completed. It can be seen that in the present invention, the coordinate transformation of the reference stator voltage is avoided, and the rotor motion is considered only based on the assumption of a constant rotor speed. Therefore, during the PWM operation, the one-step prediction is independent of the rotor motion.

[0029] Furthermore, in step S3, the reference stator flux linkage vector at the k+2 moment in the α-β axis is predicted, and the reference stator voltage at the k+1 moment is synthesized:

[0030] The synthesis steps of the reference stator flux linkage vector at the k+2 moment and the reference stator voltage at the k+1 moment are as follows:

[0031] Based on the assumption that the current remains unchanged over a short time step, that is, i d (k)* = i d (k+2)* , i q (k ), * = i q (k+2)* , the rotor position at the k+2 moment can be easily calculated as θ e (k) + 2ω e T s , and the reference stator flux linkage in the stationary coordinate system can be calculated through coordinate transformation as:

[0032]

[0033] where ψ α (k+2)* and ψ β (k+2)* are the estimated reference stator flux linkages at the k+2 moment.

[0034] Combined with the discretized current-flux linkage model in the stationary coordinate system, the voltage is expressed as:

[0035]

[0036] According to the above formula, substitute ψ α (k+1) and ψ β (k+1) with ψ α (k+2)* and ψ β (k+2)* respectively, and substitute ψ α (k) and ψ β (k) with ψ α (k+1) and ψ β (k+1) , and substitute i α (k)* and i β (k)* with i d (k+1) and i q (k+1) . After coordinate transformation, the reference stator voltage at the (k + 1)-th moment in the stationary coordinate system can be obtained:

[0037]

[0038] In the above formula, ψ α (k+2)* and ψ β (k+2)* are the reference stator fluxes at the (k + 2)-th moment, which can be obtained from S3, the values of i d (k+1) and i q (k +1) can be obtained from S2, ψ α (k+1) and ψ β (k+1) can be obtained from S1. The calculated u α (k+1)* and u β (k+1)* are the reference stator voltages at the (k + 1)-th moment, and they will return to S1 to participate in the calculation of the stator flux.

[0039] The beneficial effects of the present invention are as follows:

[0040] 1. The reference stator voltage for realizing deadbeat control in the present invention is directly obtained based on the stationary coordinate system, without coordinate transformation, which is more conducive to combining with SVPWM.

[0041] 2. The present invention avoids the voltage errors related to the two methods of not considering rotor motion compensation and considering rotor motion compensation in the traditional DBPCC.

[0042] 3. The present invention takes into account the processing delay and rotor motion effect in a high-speed permanent magnet synchronous motor drive system, and the control performance is basically not affected by high-speed operation.

[0043] 4. The controller of the present invention can achieve deadbeat control of d-q axis currents within two time steps and has no cross-coupling within the entire speed and SFR range. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a flowchart of a deadbeat predictive current control method for a high-speed permanent magnet synchronous motor at a low ratio of switching frequency to fundamental frequency according to an embodiment of the present invention.

[0045] Figure 2 It is a structural diagram of a deadbeat predictive current control method for a high-speed permanent magnet synchronous motor at a low ratio of switching frequency to fundamental frequency according to an embodiment of the present invention.

[0046] Figure 3 It is a typical timing diagram of a digital controller according to an embodiment of the present invention.

[0047] Figure 4 It is a structural diagram of a traditional deadbeat predictive current control method for comparison with the proposed method according to an embodiment of the present invention.

[0048] Figure 5 It is a schematic diagram of the speed effect of the deadbeat predictive current control method for a high-speed permanent magnet synchronous motor at a low ratio of switching frequency to fundamental frequency according to an embodiment of the present invention.

[0049] Figure 6 It is a schematic diagram of the torque effect of the deadbeat predictive current control method for a high-speed permanent magnet synchronous motor at a low ratio of switching frequency to fundamental frequency according to an embodiment of the present invention.

[0050] Figure 7 It is a schematic diagram of the d-axis current effect of the deadbeat predictive current control method for a high-speed permanent magnet synchronous motor at a low ratio of switching frequency to fundamental frequency according to an embodiment of the present invention.

[0051] Figure 8 It is a schematic diagram of the q-axis current effect of the deadbeat predictive current control method for a high-speed permanent magnet synchronous motor at a low ratio of switching frequency to fundamental frequency according to an embodiment of the present invention. SPECIFIC IMPLEMENTATION MANNER

[0052] The present invention will be further described in detail below with reference to the drawings and specific implementation manners.

[0053] Embodiment 1

[0054] Figure 1It is a flowchart of a deadbeat predictive current control method for a high-speed permanent magnet synchronous motor at a low ratio of switching frequency to fundamental frequency based on high-speed permanent magnets. Figure 2 It is a structural diagram of a deadbeat predictive current control method for a high-speed permanent magnet synchronous motor at a low ratio of switching frequency to fundamental frequency according to an embodiment of the present invention. This embodiment proposes a deadbeat predictive current control method for a high-speed permanent magnet synchronous motor at a low ratio of switching frequency to fundamental frequency. The method includes the following steps:

[0055] S1: Based on the reference d-q axis currents, the current-flux linkage model of the permanent magnet synchronous motor, and coordinate transformation, predict the stator flux linkage vector scheme at the (k + 1)th moment based on the integration of the reference stator voltage vector at the kth step.

[0056] S2: Based on the current-flux linkage model of the permanent magnet synchronous motor and the stator flux linkage at the (k + 1)th moment predicted in S1, predict the stator currents at the (k + 1)th moment in the d-q axis.

[0057] S3: Based on the assumption that the current remains unchanged over a short time step, predict the reference stator flux linkage vector at the (k + 2)th moment in the α-β axis. According to the discretized current-flux linkage equation and the stator flux linkage and stator currents at the (k + 1)th moment in S1 and S2, calculate the reference voltage at the (k + 1)th moment.

[0058] S4: A deadbeat predictive current control method for a high-speed permanent magnet synchronous motor at a low ratio of switching frequency to fundamental frequency is proposed.

[0059] I. Method for predicting the stator flux linkage vector at the (k + 1)th moment in the stationary coordinate system

[0060] As Figure 2 shown, i d (k) and i q (k) The currents are obtained by continuous coordinate transformation of the three-phase currents sampled by the current sensor and are obtained from the position sensor. Ignoring the nonlinearity of the inverter, the integral of the stator voltage over time can be assumed to be the product of the reference stator voltage and the time step. Therefore, the current-flux linkage model in the stationary coordinate system can be discretized, and the information it contains is the stator flux linkage, stator voltage, and current values at the kth moment in the stationary coordinate system, where the stator flux linkage can be obtained by coordinate transformation of the stator flux linkage at the kth moment in the synchronous rotating coordinate system, and the stator voltage is obtained by delaying the finally synthesized reference voltage at the (k + 1)th moment by one beat.

[0061] II. Method for predicting the stator currents at the (k + 1)th moment in the synchronous rotating coordinate system

[0062] As Figure 2As shown, the current expression can be obtained by transforming the current-flux linkage equation under the d-q axes. The stator flux linkage at the (k+1)-th moment under the d-q axes is obtained by coordinate transformation of the predicted stator flux linkage vector at the (k+1)-th moment under the α-β axes. Since the mechanical time constant is relatively large compared to the control time step, the motor speed can be regarded as a constant. Therefore, the rotor position at the (k+1)-th moment can be easily calculated as θ e (k) + ω e T s , and this angle is used to participate in the calculation of coordinate transformation.

[0063] III. Method for Predicting the Reference Stator Flux Linkage Vector at the (k+2)-th Moment in the Stationary Coordinate System and Synthesizing the Reference Stator Current at the (k+1)-th Moment

[0064] As Figure 2 shown, assuming that the reference current remains unchanged in a short time step, i.e., i d (k)* = i d (k+2)* , i q (k)* = i q (k+2)* , then from i d (k)* and i q (k)* , combining with the current-flux linkage equation under the d-q axes, the stator flux linkage can be obtained. After coordinate transformation, the reference value of the stator flux linkage at the (k+2)-th moment under the α-β axes can be obtained. Similarly, the rotor position at the (k+2)-th moment can be easily calculated as θ e (k) + 2ω e T s , and this angle is used to participate in the calculation of coordinate transformation.

[0065] So far, the stator flux linkage at the (k+1)-th moment in the stationary coordinate system, the stator current at the (k+1)-th moment in the synchronous rotating coordinate system, and the reference stator flux linkage at the (k+2)-th moment in the stationary coordinate system have been calculated. Combining with the equation for solving the voltage after discretizing the current-flux linkage model in the stationary coordinate system, the method for obtaining the reference stator current at the (k+1)-th moment in the stationary coordinate system can be obtained.

[0066] IV. Deadbeat Predictive Current Control Method System Based on the Ratio of Low Switching Frequency to Fundamental Frequency of High-Speed Permanent Magnet Synchronous Motor

[0067] In the embodiments of the present invention, the deadbeat predictive current control at a low switching frequency to fundamental frequency ratio of a high-speed permanent magnet synchronous motor is used, and the stability of the motor during high-speed operation is enhanced by using the proposed method, and the speed operating range is expanded. When the given initial speed is 1000 rpm, the given speed is 25000 rpm, and the working condition is to apply a load of 5 N·m at 0.6 s and a load of 2 N·m at 1.2 s. In this example, to study the worst-case scenario, the sampling frequency is set to be the same as the switching frequency, that is, single sampling and single update; the sampling frequency can also be increased to twice the switching frequency, that is, double sampling and double update. For the latter case, the movement of the rotor within the control period is reduced, so the effective SFR of the control system will increase at the given speed. When the SFR decreases to a lower value at high speed, the same analysis, results, and conclusions as those of single sampling and single update can be obtained.

[0068] Figure 5 For the simulated speed waveform diagram, the SFR at this time is about 6, compared with Figure 4 the corresponding traditional DBPCC method, it can achieve a lower SFR under the premise of instability. Figure 6 Torque simulation diagram of the motor, with a rapid torque response. Figure 7 For the reference current and actual current of the d-axis, Figure 8 For the reference current and actual current of the q-axis, it can be seen that the current reaches stability and can achieve a good tracking effect. For predictive control, to obtain good control performance, an accurate machine model needs to be adopted. However, due to the existence of inverter voltage drop and dead-time effect in the simulation, the nonlinearity of the inverter is inevitable, which leads to Figure 8 an obvious offset error in the q-axis current in

[0069] In summary, the algorithm of the present invention accurately considers the effects of sampling delay and rotor movement, and can achieve excellent deadbeat control of high-speed d-q axis currents even under very low SFR conditions. During high-speed transient processes, the d-q axis cross-coupling can be almost eliminated, and stable operation at high motor speeds can be achieved.

Claims

1. A deadbeat predictive current control method for a high-speed permanent magnet synchronous motor at a low ratio of switching frequency to fundamental frequency, comprising the following steps: S1: Based on the reference d-q axis currents, the current-flux linkage model of the permanent magnet synchronous motor, and coordinate transformation, predict the reference stator flux linkage vector at the (k + 1)-th step based on the integration of the reference stator voltage vector at the k-th step. S2: Based on the current-flux linkage model of the permanent magnet synchronous motor and the stator flux linkage at the (k + 1)-th step predicted in S1, predict the stator current at the (k + 1)-th step in the synchronous rotating coordinate system. S3: Based on the assumption that the current remains unchanged over a short time step, predict the reference stator flux linkage vector at the (k + 2)-th step in the α-β axis. Calculate the reference voltage at the (k + 1)-th step according to the discretized current-flux linkage equation and the stator flux linkage and stator current at the (k + 1)-th step in S1 and S2.

2. The control method according to claim 1, characterized in that In step S1, the scheme for predicting the reference stator flux linkage vector at the (k + 1)-th step: The steps for predicting the reference stator flux linkage vector at the (k + 1)-th step include the following: The proposed method also includes two steps, one-step prediction of stator flux linkage and current, and synthesis of the reference voltage for deadbeat control, all of which are based on the mathematical model in the stationary coordinate system. The current-flux linkage model in the stationary coordinate system is as follows: For simplicity of analysis, a surface-mounted permanent magnet synchronous motor is adopted, and the d-axis inductance is equal to the q-axis inductance, that is, L s = L d = L q , and the current-flux linkage model in the synchronous rotating coordinate system is as follows: Neglecting the nonlinearity of the inverter, the integral of the stator voltage over time can be assumed to be the product of the reference stator voltage and the time step. Therefore, using the forward Euler approximation, it can be discretized in the stationary coordinate system as: According to the principle of SVPWM, the present invention gives an accurate estimate of the voltage integral quantity, which is independent of the rotor motion. The discretization error is only determined by the estimation error of the resistive voltage drop and can be ignored at high speeds. The stator flux linkage at the k-th step in the stationary coordinate system can be obtained from the stator flux linkage at the k-th step in the synchronous rotating coordinate system through the inverse Park coordinate transformation, and the stator flux linkage at the (k + 1)-th step can be obtained by combining the discretized flux linkage equation: where T s is the switching cycle time, R is the stator resistance, L s is the synchronous inductance, ψ m is the permanent magnet flux linkage, i d ( k ) and i q ( k ) are the measured values of d-q axis currents, θ e (k) is the motor rotor position feedback value, i α (k) and i β (k) are the measured values of αβ axis currents, u α (k)* and u β (k)* are the synthesized stator voltage reference values, ψ α (k+1) and ψ β (k+1) are the predicted stator flux linkages at the next moment.

3. The control method according to claim 1, wherein In step S2, the scheme for predicting the stator current at the (k + 1)-th step in the stationary coordinate system based on the current-flux linkage model of the permanent magnet synchronous motor and the stator flux linkage at the (k + 1)-th step predicted in S1: The steps for predicting the stator current at the (k + 1)-th step: Since the mechanical time constant is relatively large compared to the control time step, the motor speed can be considered constant, and thus the rotor position at time k + 1 can be easily calculated as θ e (k) + ω e T s , and the current-flux model in the synchronous rotating coordinate system is rewritten as: Combining the above equation, and then transforming the flux linkage through the Park coordinate transformation to obtain the stator current at the (k + 1)-th step in the synchronous rotating coordinate system: where i d (k+1) and i q (k+1) are the predicted values of the d-q axis currents at the next moment. Thus far, the one-step flux linkage and one-step current prediction are completed. It can be seen that in the present invention, the coordinate transformation of the reference stator voltage is avoided, and the rotor motion is considered only based on the assumption of a constant rotor speed. Therefore, during the PWM operation, the one-step prediction is independent of the rotor motion.

4. The control method according to claim 1, wherein The scheme for predicting the reference stator flux linkage vector at the (k + 2)-th step in the α-β axis and synthesizing the reference stator voltage at the (k + 1)-th step: The steps for synthesizing the reference stator flux linkage vector at the (k + 2)-th step and the reference stator voltage at the (k + 1)-th step are as follows: Based on the assumption that the current remains constant over a short time step, i.e., i d (k)* = i d (k+2)* , i q (k)* = i q (k+2)* , the rotor position at time k + 2 can be easily calculated as θ e (k) + 2ω e T s . The reference stator flux linkage in the stationary coordinate system can be calculated through coordinate transformation as follows: where ψ α (k+2)* and ψ β (k+2)* are the estimated reference stator flux linkages at time k+2. Then, combining the discretized current-flux linkage model in the stationary coordinate system, the voltage is expressed as: According to the above formula, substitute ψ α (k+1) and ψ β (k+1) with ψ α (k+2)* and ψ β (k+2)* , substitute ψ α (k) and ψ β (k) with ψ α (k+1) and ψ β (k+1) , substitute i α (k)* and i β (k)* with i d (k+1) and i q (k+1) After coordinate transformation, the reference value of the stator voltage at the (k + 1)-th moment in the stationary coordinate system can be obtained: In the above formula, ψ α (k+2)* and ψ β (k+2)* are the reference stator flux linkages at time k + 2, which can be obtained from S3. The values of i d (k+1) and i q (k+1) can be obtained from S2. ψ α (k+1) and ψ β (k+1) can be obtained from S1. The calculated u α (k+1)* and u β (k+1)* are the reference values of the stator voltage at time k + 1, which will in turn return to S1 to participate in the calculation of the stator flux linkage.

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