Discrete modeling and positionless control method of low carrier ratio long cable permanent magnet motor

Abstract

The application discloses a low carrier ratio long cable permanent magnet motor discrete modeling and positionless control method and belongs to the motor field. In view of the problem that the resistance characteristic of a low carrier ratio long cable permanent magnet synchronous motor significantly leads to the precision reduction of a conventional average voltage model, the application decomposes a switching period into a plurality of zero-order holding voltage excitation sections according to the discrete characteristic of a converter output pulse width modulation voltage, establishes a motor accurate discrete model considering the resistance characteristic by solving the accurate current response of the permanent magnet motor section by section, further establishes a deadbeat current controller and a motor back electromotive force observer based on the discrete model, and realizes the positionless sensor operation of the low carrier ratio long cable permanent magnet synchronous motor system. The application improves the discrete modeling precision of the low carrier ratio long cable permanent magnet synchronous motor and improves the positionless control performance of the permanent magnet synchronous motor system under the working condition.

Description

Technical Field

[0001] This invention relates to motor systems, specifically disclosing a discrete modeling and positionless control method for a low carrier ratio long cable permanent magnet motor, belonging to the field of motors. Background Technology

[0002] Permanent magnet motor drive systems, with their advantages of high efficiency and compactness, have been widely used in energy industries such as coal mining. Due to the complex working environment, and for ease of equipment maintenance, the power converter drive system supplying the motor is typically deployed on the ground, while the motor itself is deployed at the work site. This necessitates long cables connecting the ground-based power converter and the on-site motor. For long-cable permanent magnet motor drive systems, obtaining rotor position information using rotor position sensors is extremely difficult, making sensorless operation a necessity. Therefore, establishing an accurate discrete model of a low-carrier-ratio long-cable permanent magnet synchronous motor is crucial for improving its positionless control performance, as it forms the basis for position observation. Existing discrete models of permanent magnet motors typically ignore resistive elements in the equivalent circuit of the permanent magnet motor, using the volt-second balance principle to approximate the pulse-width modulation voltage output by the converter as the zero-order average voltage held in a single switching cycle. Based on this, a discrete model of the permanent magnet motor is established. However, to increase productivity, the power levels of motor systems in the energy industry are constantly increasing, and the converters of long-cable permanent magnet motor systems typically operate at low switching frequencies. The significant resistance characteristics of the motor system caused by long cable operation and the low carrier ratio operation caused by low switching frequency operation will increase the modeling error of the existing average voltage model based on volt-second balance, resulting in the deterioration of the position control performance of the existing long cable low carrier ratio permanent magnet motor system. Summary of the Invention

[0003] Technical Problem: The purpose of this invention is to address the shortcomings of the aforementioned background technology by providing a discrete modeling and positionless control method for a long cable permanent magnet motor with a low carrier ratio. This method solves the technical problem of decreased observation and control performance of existing discrete models of permanent magnet motors based on the mean voltage model when used in permanent magnet motor systems operating with a long cable and a low carrier ratio, thereby achieving the invention objective of improving the positionless control performance of long cable permanent magnet motor systems with a low carrier ratio.

[0004] Technical solution: The present invention provides a discrete modeling and positionless control method for a low carrier ratio long cable permanent magnet motor, comprising the following steps:

[0005] Step 1: Decompose the pulse width modulated voltage output of the two-level voltage source converter using space vector modulation into different zero-order hold voltage excitation segments. The switching state of the power devices of the converter remains unchanged in each voltage excitation segment, so that the voltage vector output by the converter remains unchanged in each voltage excitation segment.

[0006] Step 2: Obtain the current sampling value at the start of the switching cycle through current sampling. Based on the voltage vector and initial current value of the first voltage excitation segment in Step 1, accurately solve the current value at the end of the first voltage excitation segment through the motor differential equation, which is the initial current value of the second voltage excitation segment.

[0007] Step 3: Repeat the calculation method in Step 2 to solve for the precise current value at the end of each remaining voltage excitation segment, and obtain the precise current response result at the end of the switching cycle, thereby establishing a precise discrete model of the motor on the switching cycle time scale.

[0008] Step 4: With current reference value tracking as the target, calculate the reference voltage vector based on the motor mean discrete model, and determine the effective vector to be used in the switching cycle accordingly. Obtain the preliminary solution of the effective vector and its duty cycle. Then, with current reference value tracking as the target, use the preliminary solution as the initial value for iterative calculation based on the motor accurate discrete model established in Step 3, calculate the accurate solution results of the action time of each effective vector online, and determine the duty cycle of the power device.

[0009] Step 5: Based on the reference voltage vector in Step 4, establish a mean voltage model back EMF Luenberger observer with stator current and back EMF as state variables. Calculate the current calculation difference between the mean voltage model and the piecewise discrete model under the same switching sequence, and feed it forward to the calculation formula of the current state variable in the state space equation of the back EMF Luenberger observer to obtain the back EMF observation result of the permanent magnet motor. Further use phase-locked loop technology to calculate the motor rotor position to achieve positionless control.

[0010] in,

[0011] In step 1, a two-level voltage source converter using space vector modulation is employed. The single switching cycle of the converter's power devices is divided into seven different voltage excitation segments, namely zero vector... U 0. The first valid vector The second valid vector Zero vector U 0. The second valid vector The first valid vector Zero vector U 0. There are eight points from the start time to the end time, which serve as the boundaries of each voltage excitation segment. t 0、 t 1. t 2. t 3. t 4. t 5. t 6. t 7, of which, t 0 is the start time of the switching cycle. t7 is the end time of the switching cycle; the durations of each voltage excitation segment are respectively... T 0 / 4、 , , T 0 / 2、 , T 0 / 4, T 0, and These are the zero vector and the first valid vector, respectively. and the second valid vector The total duration; the voltage vector within each voltage excitation segment remains unchanged, corresponding to the zero-order discretization method.

[0012] In step 2, the current value at the end of the first voltage excitation segment, and its current complex vector precise response calculation result are as follows:

[0013] ,

[0014] in It is the complex vector of the motor phase current in the αβ coordinate system, written as , It is the imaginary unit; superscript t 0 and t 1 represents the corresponding variable in t 0 time and t The value at time 1, R s It is the stator resistance. L s It is a synchronous inductor. ω It is the electrical angular frequency. It is the amplitude of the permanent magnet flux linkage. θ It refers to the electrical angle position of the motor rotor.

[0015] In step 3, among the precise current values ​​at the end of each remaining voltage excitation segment, the current value at the end of the second voltage excitation segment is:

[0016] ,

[0017] superscript t 2 represents the corresponding variable in t The value at time 2, let the initial value of the current be denoted as . Repeat this calculation process to obtain the end time of the switching cycle. t The current expression at time 7 is denoted as: time:

[0018] ,

[0019] inT s It is the switching cycle, superscript. and Indicates the corresponding variable in and The value of the moment. and These are two dimensionless coefficients, expressed as:

[0020] ,

[0021] In step 4, the expression for the reference voltage vector calculated based on the motor mean discrete model is as follows:

[0022] ,

[0023] in This is the reference value for the dq axis current. It is the calculated reference value of the αβ axis voltage, according to The phase in the αβ plane determines the two effective voltage vectors required for the switching cycle; since the vector sequence is centrally symmetrically arranged, the actual duration of the seven voltage excitation segments has only two degrees of freedom. T 0 and Let be the free variable to be determined, then ;by The target value is the motor phase current following the current reference value. Establish a system based on... T 0 and The system of equations:

[0024] ,

[0025] in:

[0026] ,

[0027] in:

[0028] ,

[0029] It is about T The exponent term of 0, It is about T 0 and The exponential term, A , B , W These are variables introduced to simplify expressions, where A It concerns the effective vector. The current term, B It is about The current term, WIt pertains to the current term related to the permanent magnet flux linkage, initial current value, and reference value. yes and The coefficients of the relevant terms; the system of equations was solved online using the Newton-Raphson algorithm. T 0 and The value is used to determine the duty cycle of each phase switching device; the reference voltage is then used to determine the duty cycle of each phase switching device. corresponding T 0 and Used as initial values ​​for numerical solving algorithms to accelerate the iteration speed of numerical solving algorithms.

[0030] In step 5, the expression for the mean voltage model back EMF Luenberger observer is: , ,in:

[0031] ,

[0032] It is the back EMF of the permanent magnet on the αβ axis of the motor. G , H and C These are the state matrix, input matrix, and output matrix of the discrete state-space equations for the mean voltage model, respectively. L It is the observer gain matrix. and These are two elements of the observer gain matrix. It is a state vector. It is the output vector. u It is the input vector, and the superscript "^" indicates the observed value of the corresponding variable. It is the average value of the motor αβ shaft terminal voltage during the switching cycle;

[0033] Mean voltage model and piecewise voltage model under the same switching sequence The expression for the current difference at time is: After this current difference is added as a feedforward term to the back EMF observer of the permanent magnet motor based on the mean voltage model, the back EMF observer is corrected to... .

[0034] This allows for online observation of the back electromotive force of a permanent magnet motor. Because... The expression is Therefore, phase-locked loop technology can be used to extract the motor rotor position from the observation results of permanent magnet back EMF, which can be used in motor control.

[0035] Beneficial Effects: The discrete modeling and positionless control method for a low carrier ratio long cable permanent magnet motor of the present invention, which adopts the above technical solution, has the following advantages:

[0036] (1) This invention calculates the precise response of the phase current of the permanent magnet motor under pulse width modulation voltage excitation in segments, which can accurately account for the influence of resistance characteristics on the discrete modeling of the motor, solves the problem of increased modeling error of the existing average voltage modeling method based on volt-second balance under the condition of long cable and low carrier ratio, and provides a modeling basis for improving the position control performance of long cable and low carrier ratio motor.

[0037] (2) Based on the established segmented discrete precision motor model, the present invention designs a deadbeat current controller, which can effectively improve the accuracy of current prediction under the condition of long cable and low carrier ratio. It can effectively solve the problem that the current control performance of the existing average voltage motor discrete model decreases due to the increase of discrete model error under the condition of long cable, and can improve the current control accuracy of permanent magnet motor under this condition.

[0038] (3) Based on the established segmented discrete precision motor model, the present invention designs a permanent magnet motor back EMF observer. The difference between the current calculation of the precise discrete motor model of the present invention and the existing mean voltage discrete model is fed forward to the back EMF observer, which can effectively improve the online observation accuracy of permanent magnet back EMF, improve the accuracy of motor rotor position estimation, and thus improve the motor operation performance under the condition of long cable and low carrier ratio. Attached Figure Description

[0039] Figure 1 This is a vector sequence diagram of a single switching cycle of a typical two-level converter.

[0040] Figure 2 This is a two-dimensional distribution diagram of the difference coefficients between the segmented voltage model of this invention and the existing mean voltage model with respect to cable length and switching frequency.

[0041] Figure 3 This is a two-dimensional distribution diagram of the current calculation error of the segmented voltage model of this invention and the existing average voltage model with respect to cable length and switching frequency.

[0042] Figure 4 This is a block diagram of the deadbeat control and sensorless control based on the segmented voltage model of the present invention.

[0043] Figure 5 The current prediction error waveforms of the segmented voltage model of this invention and the existing mean voltage model are experimental results when using accurate motor parameters.

[0044] Figure 6 The current prediction error waveforms of the segmented voltage model of this invention and the existing mean voltage model are experimental results when using mismatched motor parameters.

[0045] Figure 7 The results are experimental results of the existing mean voltage model and the position observation error waveform.

[0046] Figure 8This is the experimental result of the position observation error waveform of the segmented voltage model of this invention.

[0047] Figure 9 The experimental results are based on the actual rotational speed, position, and rotational speed observation error waveforms of the existing mean voltage model.

[0048] Figure 10 These are the experimental results of the actual rotational speed, position, and rotational speed observation error waveforms of the segmented voltage model of this invention.

[0049] Figure 11 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] The present invention provides a method for discrete modeling and positionless control of a low carrier ratio long cable permanent magnet motor, comprising the following steps:

[0052] like Figure 11 As shown:

[0053] Step 1: Decompose the pulse width modulated voltage output of the two-level voltage source converter using space vector modulation into different zero-order hold voltage excitation segments. The switching state of the power devices of the converter remains unchanged in each voltage excitation segment, so that the voltage vector output by the converter remains unchanged in each voltage excitation segment.

[0054] Step 2: Obtain the current sampling value at the start of the switching cycle through current sampling. Based on the voltage vector and initial current value of the first voltage excitation segment in Step 1, accurately solve the current value at the end of the first voltage excitation segment through the motor differential equation, which is the initial current value of the second voltage excitation segment.

[0055] Step 3: Repeat the calculation method in Step 2 to solve for the precise current value at the end of each remaining voltage excitation segment, and obtain the precise current response result at the end of the switching cycle, thereby establishing a precise discrete model of the motor on the switching cycle time scale.

[0056] Step 4: With current reference value tracking as the target, calculate the reference voltage vector based on the motor mean discrete model, and determine the effective vector to be used in the switching cycle accordingly. Obtain the preliminary solution of the effective vector and its duty cycle. Then, with current reference value tracking as the target, use the preliminary solution as the initial value for iterative calculation based on the motor accurate discrete model established in Step 3, calculate the accurate solution results of the action time of each effective vector online, and determine the duty cycle of the power device.

[0057] Step 5: Based on the reference voltage vector in Step 4, establish a mean voltage model back EMF Luenberger observer with stator current and back EMF as state variables. Calculate the current calculation difference between the mean voltage model and the piecewise discrete model under the same switching sequence, and feed it forward to the calculation formula of the current state variable in the state space equation of the back EMF Luenberger observer to obtain the back EMF observation result of the permanent magnet motor. Further use phase-locked loop technology to calculate the motor rotor position to achieve positionless control.

[0058] like Figure 1 The diagram shown is a typical vector sequence of a single switching cycle in a two-level converter. A single switching cycle can be divided into seven different voltage excitation segments, namely the zero vector... U 0. The first valid vector The second valid vector Zero vector U 0. The second valid vector The first valid vector Zero vector U 0. There are eight points from the start time to the end time, which serve as the boundaries of each voltage excitation segment. t 0~ t 7. The durations of each voltage excitation segment are as follows: T 0 / 4、 , , T 0 / 2、 , , T 0 / 4, the voltage vector within each voltage excitation segment remains unchanged, corresponding to the zero-order discrete method.

[0059] Furthermore, the calculated result of the complex vector exact response of the motor phase current at the end of the first voltage excitation segment is as follows:

[0060] (1)

[0061] in It is the complex vector of the motor phase current in the αβ coordinate system, which can be written as , It is the imaginary unit. (Superscript) t 0 and t 1 represents the corresponding variable int 0 time and t The value at time 1, R s It is the stator resistance. L s It is a synchronous inductor. ω It is the electrical angular frequency. It is the amplitude of the permanent magnet flux linkage. θ It refers to the position of the motor rotor in electrical angle form.

[0062] Furthermore, by repeating step 2 and the current response solution method, the current value at the end of the second voltage excitation segment is calculated.

[0063] (2)

[0064] superscript t 2 represents the corresponding variable in t The value at time 2 will exist t Substituting the expression at time 1 into its... t The expression for time 2 is obtained

[0065] (3)

[0066] This yields information based on the initial current value and the applied voltage vector. t Current value at time 2. Let the initial current value be denoted as _____. Repeating this calculation process yields... t The expression for the current value at time 7 is denoted as: time:

[0067] (4)

[0068] in T s It is the switching cycle, superscript. and Indicates the corresponding variable in and The numerical value at time. Among them, and There are two dimensionless coefficients, expressed as follows:

[0069] (5)

[0070] The precise discrete model of the motor has now been established.

[0071] like Figure 2 The diagram shows a two-dimensional distribution of the difference coefficients between the segmented voltage model of this invention and the existing mean voltage model with respect to cable length and switching frequency. The expression for the existing mean voltage discrete model is:

[0072] (6)

[0073] Taking the voltage vector sequence of a two-level converter in the first sector as an example, the expressions for the two effective vectors are:

[0074] (7)

[0075] in U dc This is the DC bus voltage. Therefore, the existing mean voltage model and the piecewise discrete voltage model established in this invention... The current difference at time t is:

[0076] (8)

[0077] Among them, the current error coefficient E U The expression is:

[0078] (9)

[0079] Furthermore, in order to analyze the current error coefficient E U A quantitative analysis of the effects of varying cable length and switching frequency on existing long-cable, low-carrier-ratio permanent magnet motor system parameters is conducted. The cable resistance is 0.1373 Ω / km, the cable inductance is 0.1998 mH / km, the motor stator resistance is 0.0772 Ω, the synchronous inductance is 1.3 mH, and the DC bus voltage is 311.1 V. The cable length ranges from 1 to 10 km, and the switching frequency ranges from 0.2 to 1.0 kHz. Current error coefficient... E U Analysis results as follows Figure 2 As shown, the current error coefficient increases with increasing cable length and decreasing switching frequency. E U It shows a clear upward trend.

[0080] like Figure 3 The diagram shows a two-dimensional distribution of the current calculation error of the segmented voltage model of the present invention and the existing average voltage model with respect to cable length and switching frequency. The expression for the current calculation error is shown in equation (8). Figure 2 Same motor system parameters. From Figure 3 It can be seen that as the cable length increases and the switching frequency decreases, the current calculation error of the two modes gradually increases, reaching a maximum of about 6A, which is very significant compared to the rated current of the motor of 16.9A. Figure 2 and Figure 3The analysis results show that under the condition of long cable and low carrier ratio, the modeling error of the existing mean voltage model will rise to a non-negligible level. It is necessary to use the segmented voltage accurate discrete modeling method provided by this invention for the design of motor controller and observer.

[0081] like Figure 4 The block diagram shown is for deadbeat control and sensorless control based on a piecewise voltage model. The first step of deadbeat control is to calculate the reference voltage vector using the average voltage model to determine the effective and zero vectors output in the current switching cycle. The second step is to establish a deadbeat current tracking equation based on the selected effective and zero vectors using a piecewise voltage discrete model, and then iteratively solve it online using the Newton-Raphson method to obtain the final duty cycle of the effective and zero vectors. Regarding motor rotor position observation, the difference between the current calculated by the average voltage model and the piecewise voltage model under the currently executed pulse-width modulation voltage is first calculated. This current difference is then fed forward to a permanent magnet back EMF observer based on the average voltage model to correct the modeling error of the average voltage model. Finally, a phase-locked loop (PLL) technique is used to extract the motor rotor position from the observed permanent magnet back EMF for use in motor control. Specifically, in the first step of deadbeat control, the expression for calculating the reference voltage vector based on the motor's average discrete model with current reference value tracking as the target is:

[0082] (10)

[0083] in This is the reference value for the dq axis current. This is the calculated reference value for the αβ axis voltage. According to... The phase in the αβ plane can determine the two effective voltage vectors required for the switching cycle. When When the phase is between 0 and 60 degrees, the reference voltage vector is located in the first sector, and the effective vector numbers are 100 and 110; when When the phase is between 60 and 120 degrees, the reference voltage vector is located in the second sector, and the effective vector numbers are 110 and 010; when When the phase is between 120 and 180 degrees, the reference voltage vector is located in the third sector, and the effective vector numbers are 010 and 011; when When the phase is between 180 and 240 degrees, the reference voltage vector is located in the fourth sector, and the effective vector numbers are 011 and 001; when When the phase is between 240 and 300 degrees, the reference voltage vector is located in the fifth sector, and the effective vector numbers are 001 and 101; when When the phase is between 300 and 360 degrees, the reference voltage vector is located in the fifth sector, and the effective vectors are numbered 101 and 100. "1" indicates that the upper transistor in the bridge arm is on and the lower transistor is off, and "0" indicates that the lower transistor in the bridge arm is on and the upper transistor is off. The three-digit numbers are arranged in the order of phases A, B, and C. Furthermore, in the second step of deadbeat control, since the vector sequence is centrally symmetrically arranged, the actual action time of the seven voltage excitation segments only has two degrees of freedom. T 0 and Taking free variables as an example, we have .by With the constant motor phase current following the reference current as the target, a system of equations can be established as follows:

[0084] (11)

[0085] in:

[0086] (12)

[0087] Solving this system of equations online yields the following results. T 0 and The value of the reference voltage is used to determine the duty cycle of each phase switching device. The solution method can use numerical algorithms such as Newton-Raphson, which can be achieved by using the reference voltage... The corresponding vector action time is used as the initial value for the numerical solution algorithm to accelerate the iteration speed of the numerical solution algorithm.

[0088] Furthermore, in the observation of the motor rotor position, the expression for the mean voltage model back EMF observer is:

[0089] (13)

[0090] in:

[0091] (14)

[0092] This is the permanent magnet back EMF of the motor's αβ axis. Furthermore, the expression for the difference in current calculation between the calculated mean voltage model and the piecewise discrete model under the same switching sequence is:

[0093] (15)

[0094] After this current difference is added as a feedforward term to the back EMF observer of the permanent magnet motor, the expression of the observer is:

[0095] (16)

[0096] This allows for online observation of the back electromotive force of a permanent magnet motor. Because... The expression is Therefore, phase-locked loop technology can be used to extract the motor rotor position from the observation results of permanent magnet back EMF, which can be used in motor control.

[0097] like Figure 5 The diagram shows experimental results of the current prediction error waveforms of the segmented voltage model provided by this invention and the existing average voltage model when using accurate motor parameters. In the experiment, the motor control algorithm was executed in a DSP TI-TMS320C28346. An additional resistor and inductor were added in series to simulate the long cable condition. Motor system resistance... R s The impedance is 0.93Ω, the synchronous inductance is 1.32mH, and the equivalent cable length is approximately 4.2km. The permanent magnet flux linkage amplitude is 0.204Wb. The converter power device switching frequency is 500Hz, the motor speed is 1000rpm, and the fundamental operating frequency is 50Hz; therefore, the carrier ratio is 10. The online current prediction error directly reflects the accuracy of the discrete motor model used. From Figure 5 It can be seen that when the motor parameters are accurate, the fluctuation amplitude of the current prediction error of the existing mean voltage model is significantly higher than that of the segmented voltage model provided by this invention, indicating that the segmented voltage model is more accurate under the current operating conditions.

[0098] like Figure 6 The experimental results shown are the current prediction error waveforms of the segmented voltage model provided by this invention and the existing mean voltage model when using mismatched motor parameters. The resistance parameter used in the controller is 20% smaller than the measured value. The experimental waveforms show that when the motor parameters are mismatched, the fluctuation amplitude of the current prediction error of the segmented voltage model is slightly higher than when the parameters are accurate, but still significantly smaller than that of the mean voltage model. Therefore, Figure 5 and Figure 6 The experimental results verify that the segmented voltage discrete model provided by this invention has higher accuracy than the mean voltage discrete model under the condition of long cable and low carrier ratio.

[0099] like Figure 7 and Figure 8 The experimental results of the position observation error waveforms of the existing mean voltage model and the piecewise voltage model provided by this invention are shown. The superscript "^" indicates the observed value of the corresponding variable, and the superscript "~" indicates the observation error of the corresponding variable. From... Figure 7 and Figure 8 The experimental results show that when the segmented voltage model provided by this invention is used to perform feedforward correction on the rotor position observation of the mean voltage model, the peak-to-peak value of the rotor position observation error fluctuation is significantly reduced, which verifies the improvement effect of the segmented voltage model provided by this invention on the motor position observation performance under the condition of long cable and low carrier ratio.

[0100] like Figure 9 and Figure 10 The experimental results of actual rotational speed, position, and rotational speed observation error waveforms are shown for the existing mean voltage model and the piecewise voltage model provided by this invention. Figure 9 and Figure 10 As can be seen, the motor speed increases from 500 rpm to 1000 rpm during the dynamic process. After using the piecewise voltage model provided by this invention to perform feedforward correction on the rotor position observation of the mean voltage model, the peak-to-peak values ​​of the speed observation error and rotor position observation error fluctuations under both steady-state and dynamic conditions of the motor are significantly reduced. This helps to reduce the impact of motor rotor position observation error fluctuations on control performance, verifying the improvement effect of the piecewise voltage model provided by this invention on motor position observation performance under long cable and low carrier ratio conditions.

[0101] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A method for discrete modeling and positionless control of a low carrier ratio long cable permanent magnet motor, characterized in that, Includes the following steps: Step 1: Decompose the pulse width modulated voltage output of the two-level voltage source converter using space vector modulation into different zero-order hold voltage excitation segments. The switching state of the power devices of the converter remains unchanged in each voltage excitation segment, so that the voltage vector output by the converter remains unchanged in each voltage excitation segment. Step 2: Obtain the current sampling value at the start of the switching cycle through current sampling. Based on the voltage vector and initial current value of the first voltage excitation segment in Step 1, accurately solve the current value at the end of the first voltage excitation segment through the motor differential equation, which is the initial current value of the second voltage excitation segment. Step 3: Repeat the calculation method in Step 2 to solve for the precise current value at the end of each remaining voltage excitation segment, and obtain the precise current response result at the end of the switching cycle, thereby establishing a precise discrete model of the motor on the switching cycle time scale. Step 4: With current reference value tracking as the target, calculate the reference voltage vector based on the motor mean discrete model, and determine the effective vector to be used in the switching cycle accordingly. Obtain the preliminary solution of the effective vector and its duty cycle. Then, with current reference value tracking as the target, use the preliminary solution as the initial value for iterative calculation based on the motor accurate discrete model established in Step 3, calculate the accurate solution results of the action time of each effective vector online, and determine the duty cycle of the power device. Step 5: Based on the reference voltage vector in Step 4, establish a mean voltage model back EMF Luenberger observer with stator current and back EMF as state variables. Calculate the current calculation difference between the mean voltage model and the piecewise discrete model under the same switching sequence, and feed it forward to the calculation formula of the current state variable in the state space equation of the back EMF Luenberger observer to obtain the back EMF observation result of the permanent magnet motor. Further use phase-locked loop technology to calculate the motor rotor position to achieve positionless control. The expression for the back electromotive force Lumberjack observer of the mean voltage model is as follows: L = [l1, l2] T ,in: x=[i αβ e αβ ] T ,u=[u αβ 0] T ,y=i αβ , e αβ This represents the back EMF of the permanent magnet on the α and β axes of the motor. G, H, and C are the state matrix, input matrix, and output matrix of the discrete state-space equations of the mean voltage model, respectively. L is the observer gain matrix, and l1 and l2 are two elements of the observer gain matrix. x is the state vector, y is the output vector, and u is the input vector. The superscript "^" indicates the observed value of the corresponding variable. αβ It is the average value of the voltage at the αβ shaft end of the motor during the switching cycle; The mean voltage model and the piecewise voltage model under the same switching sequence (k+1)T s The expression for the current difference at time is: After the current difference is added as a feedforward term to the back EMF observer of the permanent magnet motor based on the mean voltage model, the back EMF observer is corrected to... L = [l1, l2] T .

2. The method for discrete modeling and positionless control of a low carrier ratio long cable permanent magnet motor according to claim 1, characterized in that, In step 1, a two-level voltage source converter with space vector modulation is used. The single switching cycle of the converter's power device is divided into seven different voltage excitation segments, namely zero vector U0, the first effective vector U0, and so on. αβx The second effective vector U αβy Zero vector U0, second effective vector U αβy The first effective vector U αβx The zero vector U0 has eight points from start to end, serving as the boundaries of each voltage excitation segment: t0, t1, t2, t3, t4, t5, t6, and t7. Here, t0 is the start of the switching cycle, and t7 is the end of the switching cycle. The durations of each voltage excitation segment are T0 / 4, T... x / 2、T y / 2、T0 / 2、T y / 2、T x / 2、T0 / 4,T0,T x and T y These are the zero vector and the first valid vector U, respectively. αβx and the second effective vector U αβy The total duration; the voltage vector within each voltage excitation segment remains unchanged, corresponding to the zero-order discretization method.

3. The method for discrete modeling and positionless control of a low carrier ratio long cable permanent magnet motor according to claim 2, characterized in that, In step 2, the current value at the end of the first voltage excitation segment, and its current complex vector precise response calculation result are as follows: Where i αβ It is the complex vector of the motor phase current in the αβ coordinate system, written as i αβ =i α +ji β j is the imaginary unit; the superscripts t0 and t1 represent the values ​​of the corresponding variable at time t0 and t1, respectively, R s It is the stator resistance, L s It is a synchronous inductor, ω is the electrical angular frequency, and ψ is the synchronous inductor. f θ is the amplitude of the permanent magnet flux linkage, and θ is the electrical angle position of the motor rotor.

4. The method for discrete modeling and positionless control of a low carrier ratio long cable permanent magnet motor according to claim 3, characterized in that, In step 3, among the precise current values ​​at the end of each remaining voltage excitation segment, the current value at the end of the second voltage excitation segment is: The superscript t2 represents the value of the corresponding variable at time t2, and the initial value of the current is denoted as kT. s Repeating this calculation process yields the current expression at the end of the switching cycle, i.e., time t7, denoted as (k+1)T. s time: Where T s It refers to the switching period, where the superscripts k and k+1 indicate the corresponding variable in kT. s and (k+1)T s The value at time, E Tx and E Ty These are two dimensionless coefficients, expressed as: The precise discrete model of the motor has now been established.

5. The method for discrete modeling and positionless control of a low carrier ratio long cable permanent magnet motor according to claim 4, characterized in that, In step 4, the expression for the reference voltage vector calculated based on the motor mean discrete model is as follows: Where i dqref This is the dq-axis current reference value, u αβref It is the calculated reference value of the αβ axis voltage, based on u αβref The phase in the αβ plane determines the two effective voltage vectors required for the switching cycle; since the vector sequence is centrally symmetrically arranged, the actual duration of the seven voltage excitation segments has only two degrees of freedom, with T0 and T... x Let T be the free variable to be determined. y =T s -T0-T x ; with (k+1)T s The target value is the motor phase current following the current reference value. Establish a reference value for T0 and T2. x The system of equations: k1 / x1+k2x1+k3 / x2+k4x2-W1=0 k5 / x1+k6x1+k7 / x2+k8x2-W2=0, in: k3=-K(A)+K(B), k7<-Im(A)+Im(B), W1 = Re(W), W2 = Im(W) in: x1 is the exponential term with respect to T0, and x2 is the exponential term with respect to T0 and T. x The exponential term, A, B, and W, are variables introduced to simplify the expression, where A is the exponential term with respect to the effective vector U. αβx The current term, B, is about U. αβy The current term, W, is a current term relating to the permanent magnet flux linkage, the initial current value, and the reference value; k1 to k8 are the coefficients of the terms related to x1 and x2; the system of equations is solved online using the Newton-Raphson algorithm to obtain T0 and T... x The value is used to determine the duty cycle of each phase switching device; the reference voltage u is then used. αβref The corresponding T0 and T x Used as initial values ​​for numerical solving algorithms to accelerate the iteration speed of numerical solving algorithms.

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