Sensorless control angle compensation method for dual three-phase permanent magnet synchronous motor

Abstract

The application relates to a permanent magnet synchronous motor design technology, and aims to solve the problem that the angle estimation is inaccurate when a double three-phase permanent magnet synchronous motor is controlled without a position sensor in the case of inductance asymmetry, realize position estimation, online identification of the asymmetrical inductance, and compensation of the angle in position demodulation, and the angle compensation method for double three-phase permanent magnet synchronous motor control without a position sensor comprises the following steps: step one, constructing a mathematical model of the double three-phase permanent magnet synchronous motor; step two, constructing an expression about d-q inductance in the case of inductance asymmetry by using high-frequency response current sampling values, and identifying the asymmetrical L d ′ q ′ inductance parameters; and step three, combining the inductance identification result, calculating the deviation amount of the asymmetrical d-q inductance, and eliminating the deviation amount in position demodulation. The application mainly applies to permanent magnet synchronous motor design and manufacturing occasions.

Description

Technical Field

[0001] This invention relates to permanent magnet synchronous motor design technology, specifically to a control method for a dual three-phase permanent magnet synchronous motor. When the motor inductance is asymmetrical, a sensorless control method combining inductance identification and compensation angle is adopted. Background Technology

[0002] With the continuous development of AC drive systems, high-power control systems have gradually become a research hotspot. The application of traditional three-phase permanent magnet synchronous motors driven by two-level inverters in high-power applications is becoming increasingly difficult. Therefore, in recent years, multiphase motors, with their low-voltage and high-power characteristics, have attracted increasing attention from scholars. In addition, multiphase motors also have the characteristics of high output electromagnetic torque ripple frequency and low torque ripple; compared with three-phase motors, multiphase motors also have higher degrees of freedom, allowing for more flexible fault-tolerant methods to address problems such as phase loss. Among multiphase motors, the most widely studied is the dual three-phase permanent magnet synchronous motor. The dual three-phase permanent magnet synchronous motor has two sets of windings shifted by 30°, a structure that eliminates the sixth harmonic torque ripple of the motor, making the output torque more stable.

[0003] Reliable operation of permanent magnet synchronous motors requires accurate rotor position angles. Traditional motor control uses mechanical sensors to detect these angles, such as incremental photoelectric encoders and Hall effect sensors. However, these sensors not only increase the system's size and cost but are also susceptible to environmental influences, leading to inaccuracies and even damage, potentially causing motor malfunctions. Therefore, to avoid these problems, research into sensorless control technology for observing the rotor position angle of permanent magnet motors is of great significance.

[0004] Inaccurate machining of motor windings can lead to phase inductance asymmetry, most commonly single-phase inductance asymmetry. This asymmetry causes changes in the motor's dq-axis inductance. During motor control, the presence of asymmetrical inductance in the current affects stable motor operation. In sensorless control, due to the high accuracy requirements of this technology, the high-frequency response current used for position estimation can be affected by inductance asymmetry, leading to errors and impacting rotor position angle estimation. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention aims to solve the problem of inaccurate angle estimation in sensorless control of dual three-phase permanent magnet synchronous motors with inductance asymmetry. A sensorless control method using orthogonal square wave injection is proposed. This method can simultaneously identify asymmetrical inductance online and compensate for angle during position demodulation, thus improving the accuracy of the estimated position and enhancing the performance of sensorless control. Therefore, the technical solution adopted by this invention is a sensorless control angle compensation method for dual three-phase permanent magnet synchronous motors, with the following steps:

[0006] Step 1: Construct a mathematical model of a dual three-phase permanent magnet synchronous motor and derive the expression for the dq-axis inductance when the inductance is asymmetrical. Inject orthogonal square waves into the α-β axes of the stationary coordinate system, where dq and α-β are the coordinate systems obtained by rotating the natural coordinate system through Park and Clark transformations, respectively. The Park transformation is the coordinate transformation matrix from the stationary coordinate system to the rotating coordinate system, and the Clark transformation is the coordinate transformation matrix from the natural coordinate system to the stationary coordinate system. Sample the high-frequency current response four times during each square wave injection cycle. Construct an expression for the rotor position information using the sampled high-frequency response current values ​​and demodulate the rotor position angle.

[0007] Step 2: Construct an expression for the dq inductance when the inductance is asymmetrical using the high-frequency response current sampling values, and identify the asymmetrical L. d ′-L q Inductance parameters, L d ′ is the d-axis asymmetrical inductance, L q ′ represents the q-axis asymmetrical inductance;

[0008] Step 3: Based on the inductance identification results, calculate the deviation of the inductance asymmetry dq, and eliminate the deviation during position demodulation to improve the accuracy of rotor position estimation without position sensors.

[0009] In step one, the mathematical model of the dual three-phase permanent magnet synchronous motor is constructed as follows:

[0010]

[0011] In the formula, u dh u qh and u x u y These represent the high-frequency voltage signals injected along the d-axis and q-axis, and the xy harmonic subplane voltages, respectively; i dh i qh and i x i y These represent the d-axis and q-axis high-frequency current response components and the xy harmonic subplane currents, respectively; L d L q These are the high-frequency inductance values ​​for the d-axis and q-axis, respectively; L z For motor leakage inductance;

[0012] The expression for the inductance dq when the inductance is asymmetrical is:

[0013]

[0014] In the formula, L d ′、L q' is the dq inductance when the inductance is unbalanced; ΔL is the unbalanced inductance; θ is the rotor position angle.

[0015] The orthogonal square wave voltage signal injected into the α-β axes of the stationary coordinate system without position sensor control is:

[0016]

[0017] In the formula, V h The value of the injected square wave is T; the period of the injected square wave is n; and the injection order is n.

[0018] The expression for the sampled high-frequency response current is:

[0019]

[0020] In the formula, Δi αh and Δi βh L0 is the high-frequency current difference between two adjacent sampling points; L0 is the average inductance, L0 = (L d +L q ) / 2; L1 is the differential inductance, L1 = (L d -L q ) / 2; t is the number of samples;

[0021] By constructing a reasonable expression for the sampled values, we obtain an expression for θ, specifically as follows:

[0022]

[0023]

[0024] Take I sinθ For example, in the construction: at t=1, the current difference Δi of the square wave response along the α axis is selected at time t=1. αh t1 Subtract the current difference Δi along the β axis of the injected square wave response at time t=4. βh t4 At t=2, the current difference Δi in the β-axis of the injected square wave response is selected at time t=2. βh t2 Add the current difference Δi along the α axis of the injected square wave response at time t=1 αh t1 And so on, constructing I sinθ I cosθ The expression is:

[0025]

[0026] After rotor position demodulation, the expression F′ for Δθ is obtained. Δθ for:

[0027]

[0028] In the formula, Δθ represents the difference between the actual rotor angle θ and the estimated rotor angle. The discrepancy arises due to inductance asymmetry, resulting in a deviation in the demodulation and inaccurate position estimation. The rotor position angle is then obtained after processing by a phase-locked loop.

[0029] The detailed steps of step two are as follows: Construct I using the sampled values. L0 and I L1 The function, specifically its construction process, is as follows:

[0030]

[0031]

[0032] I L0 with I sinθ I cosθ The construction process is the same: at t=1, the current difference Δi of the square wave response on the β axis is selected at time t=1. βh t1 Subtract the current difference Δi in the α-axis of the injected square wave response at time t=4. αh t4 At t=2, the current difference Δi in the α-axis of the injected square wave response is selected at time t=2. αh t2 Adding the current difference Δi along the β axis of the injected square wave response at time t=1 βh t1 And so on; I L1 Then it is the constructed current I sinθ I cosθ The arithmetic square root of the sum of squares;

[0033] Construct I L0 and I L1 The expression is:

[0034]

[0035] Identify L through mathematical operations d ′-L q The inductance parameters are:

[0036]

[0037] In step three, the asymmetry L is calculated based on the inductance identification results. d ′、L q Inductance deviation of ′:

[0038]

[0039] In the formula, ΔL d and ΔL q The inductance deviation caused by asymmetry; the inductance deviation is expressed from the position demodulation formula F′. Δθ Mid-compensation, the expression after compensation H Δθ for:

[0040]

[0041] Finally, the accurate rotor position angle is obtained through phase-locked loop processing.

[0042] The features and beneficial effects of this invention are:

[0043] This invention enables sensorless control of dual three-phase permanent magnet synchronous motors, reducing motor costs, system size, and avoiding the environmental impact issues of mechanical sensors, thus making motor operation more stable. When the motor inductance is asymmetrical, the proposed compensation method can compensate for the estimated position, eliminating angle errors and ensuring accurate position estimation, thereby improving sensorless control performance. This invention is also easy to implement in engineering applications. Attached image description:

[0044] Figure 1 This is a structural diagram of a dual three-phase permanent magnet synchronous motor system;

[0045] Figure 2 Control strategy block diagram;

[0046] Figure 3 Diagram of injected orthogonal square wave voltage signal;

[0047] Figure 4 This is a schematic diagram of rotor position demodulation.

[0048] Figure 5 For the construction of I sinθ I cosθ Current simulation waveform;

[0049] Figure 6 For the construction of I L0 I L1 Current waveform diagram;

[0050] Figure 7 The simulation waveform of the angle estimation error in sensorless control when the inductance is asymmetrical;

[0051] Figure 8 The simulation waveform diagram shows the error of the estimated angle after compensation without a position sensor. Detailed Implementation

[0052] The present invention provides a sensorless control angle compensation method for a dual three-phase permanent magnet synchronous motor, comprising the following steps:

[0053] Step 1: Construct a mathematical model of a dual three-phase permanent magnet synchronous motor and derive the expression for the dq-axis inductance when the inductance is asymmetrical. Inject orthogonal square waves into the α-β axes of the stationary coordinate system, where dq and α-β are the coordinate systems obtained by rotating the natural coordinate system through Park and Clark transformations, respectively. The Park transformation is the coordinate transformation matrix from the stationary coordinate system to the rotating coordinate system, and the Clark transformation is the coordinate transformation matrix from the natural coordinate system to the stationary coordinate system. Sample the high-frequency current response four times during each square wave injection cycle. Construct an expression for rotor position information using the sampled high-frequency response current values ​​and demodulate the rotor position angle to achieve sensorless control.

[0054] Step 2: Construct an expression for the dq inductance when the inductance is asymmetrical using the high-frequency response current sampling values, and identify the asymmetrical L. d ′-L q Inductance parameters.

[0055] Step 3: Based on the inductance identification results, calculate the deviation of the inductance asymmetry dq, eliminate the deviation during position demodulation, and improve the accuracy of rotor position estimation.

[0056] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0057] The sensorless control method for dual three-phase motors of the present invention includes the following steps:

[0058] Step 1: Construct a mathematical model of the dual three-phase permanent magnet synchronous motor. The overall system structure is as follows: Figure 1 As shown, the motor drive consists of 6 bridge arms, corresponding to 2 6 =64 switching states. The sensorless control method injects orthogonal square waves into the α-β axes of the stationary coordinate system, and samples the high-frequency current response four times in each square wave injection cycle; it uses the sampled high-frequency response current values ​​to construct an expression for rotor position information, and demodulates the rotor position angle to achieve sensorless control.

[0059] In step one, the mathematical model of the dual three-phase permanent magnet synchronous motor is as follows:

[0060]

[0061] In the formula, u dh u qh and u x u y These represent the high-frequency voltage signals injected along the d-axis and q-axis, and the xy harmonic subplane voltages, respectively; i dhi qh and i x i y These represent the d-axis and q-axis high-frequency current response components and the xy harmonic subplane currents, respectively; L d L q These are the high-frequency inductance values ​​for the d-axis and q-axis, respectively; L z This refers to the leakage inductance of the motor.

[0062] Due to the asymmetry of the motor inductance, the dq-axis inductance changes. This leads to the derivation of the expression for the dq-axis inductance due to inductance asymmetry. The transformed L... d L q The expression for inductance is:

[0063]

[0064] In the formula, L d ′、L q ′ is the dq inductance when the inductance is unbalanced; ΔL is the unbalanced inductance; θ is the rotor position angle.

[0065] When the motor is running at low speed, the sensorless control method mainly utilizes the principle of salient polarity of the motor: a high-frequency voltage signal is injected into the motor, causing the motor to respond with a high-frequency current containing the rotor position. The current is then sampled and demodulated to obtain the rotor position angle.

[0066] Orthogonal square wave voltage signals injected into the α-β axes of the stationary coordinate system, such as Figure 3 As shown, its expression is:

[0067]

[0068] In the formula, V h The voltage amplitude of the injected square wave is T; T is the period of the injected square wave, which is the PWM carrier period T. s Four times; n is the injection order. Orthogonal square wave signals are injected into the α-β axes of the stationary coordinate system, and the relationship between the response current and voltage is derived as follows:

[0069]

[0070] In the formula, L0 is the average inductance, L0 = (L d +L q ) / 2; L1 is the differential inductance, L1 = (L d -L q ) / 2. The expression for the sampled high-frequency response current is:

[0071]

[0072] In the formula, Δi αh and Δi βhLet θ be the high-frequency current difference between two adjacent sampling points; t be the number of samplings. By constructing a reasonable expression for the sampled values, we obtain the following structure:

[0073]

[0074]

[0075] Take I sinθ Taking the construction as an example: at t=1, select the current difference Δi in the α-axis response of the injected square wave signal at time t=1. αh t1 Subtract the current difference Δi in the β-axis response of the injected square wave signal at time t=4. βh t4 At t=2, the current difference Δi in the β-axis response of the injected square wave signal at time t=2 is selected. βh t2 Adding the current difference Δi in the α-axis response of the injected square wave signal at time t=1 αh t1 At t=3, the injected square wave signal response at time t=3 corresponds to the α-axis current difference Δi. αh t3 The negative value, plus the current difference Δi in the β-axis response of the injected square wave signal at time t=2. βh t2 At t=4, the injected square wave signal response at time t=4 is selected to be at the β-axis current difference Δi. βh t4 The negative value, minus the current difference Δi in the α-axis response of the injected square wave signal at time t=3. αh t3 And so on, I cosθ Construct I using the same method. sinθ I cosθ Current waveform as follows Figure 5 As shown, the expression is:

[0076]

[0077] After rotor position demodulation, the expression F′ for Δθ is obtained. Δθ for:

[0078]

[0079] In the formula, Δθ represents the difference between the actual rotor angle θ and the estimated rotor angle. The difference. When the error is small enough, sin2Δθ≈sin2Δθ, and the rotor position angle is extracted using a phase-locked loop (PLL). Due to inductance asymmetry, there is a deviation in the demodulation, resulting in inaccurate position estimation.

[0080] Step 2: To compensate for the angle estimation error in sensorless control, an expression for the inductance dq is constructed using the high-frequency response current sampling value, and the asymmetry L is identified. d ′-L q Inductance parameters.

[0081] In step two, the high-frequency current sampling values ​​are used to construct the mean inductance I. L0 Sum of difference inductance I L1 The current. I L0 and I L1 The process of constructing an electric current is as follows:

[0082]

[0083]

[0084] I L0 with I sinθ I cosθ The construction process is the same: at t=1, the current difference Δi in the β-axis response of the injected square wave signal at time t=1 is selected. βh t1 Subtract the current difference Δi in the α-axis response of the injected square wave signal at time t=4. αh t4 At t=2, the current difference Δi in the α-axis response of the injected square wave signal at time t=2 is selected. αh t2 Adding the current difference Δi in the β-axis response of the injected square wave signal at time t=1 βh t1 At t=3, the injected square wave signal response at time t=3 is selected to be at the β-axis current difference Δi. βh t3 The negative value, plus the current difference Δi in the α-axis response of the injected square wave signal at time t=2. αh t2 At t=4, the injected square wave signal response at time t=4 corresponds to the α-axis current difference Δi. αh t4 The negative value, minus the current difference Δi in the β-axis response of the injected square wave signal at time t=3. βh t3 I L1 Then it is the constructed current I sinθ I cosθ The arithmetic square root of the sum of squares.

[0085] Construct the waveforms of the two currents as follows Figure 6 As shown, the expressions are as follows:

[0086]

[0087] Combining the above-constructed I sinθ I cosθ and I L0 I L1 Four types of current, derive about L d ′-L q The expression for inductance is:

[0088]

[0089] Step 3: Based on the inductance identification results, calculate the dq inductance deviation when the inductance is asymmetrical. Eliminate the deviation during position demodulation to improve the accuracy of rotor position estimation.

[0090] In step three, based on the inductance identification results and combined with the L of the inductance-symmetric motor... d L q Parameters, calculate the asymmetric L d ′、L q Inductance deviation:

[0091]

[0092] In the formula, ΔL d and ΔL q The inductance deviation caused by asymmetry; the inductance deviation is expressed from the position demodulation formula F′. Δθ Compensation, such as Figure 4 As shown, the compensated expression H Δθ for:

[0093]

[0094] The inductance deviation in the denominator is difficult to compensate for. Calculations show that when the inductance is slightly asymmetrical, the ΔL in the denominator expansion is significant. 2 ΔLL d and ΔLL q Much smaller than L d and L q This can be ignored. The overall control flow of the sensorless control method for the dual three-phase permanent magnet synchronous motor is as follows: Figure 2 As shown.

[0095] To verify the effectiveness of the sensorless control compensation method for the dual three-phase permanent magnet synchronous motor proposed in this invention, a mathematical model of the aforementioned dual three-phase permanent magnet synchronous motor and a simulation model of the sensorless control compensation method were built on the Matlab / Simulink platform. Detailed parameters of the dual three-phase permanent magnet synchronous motor used in the simulation are shown in Table 1.

[0096] Table 1 Motor Parameters

[0097]

[0098] The calculation period T of the control algorithm in the simulation s The simulation cycle is 100 μs, while the calculation cycle of the simulation model excluding the control algorithm is 1 μs. The dual three-phase permanent magnet synchronous motor operates stably at a reference speed of 200 r / min and a load torque of 10 N·m. Under the condition of asymmetrical inductance ΔL = 3 mH, the effectiveness of the proposed method is verified by comparing the estimated position error before and after sensorless control compensation.

[0099] The first operating condition is when the inductance is unbalanced, and the verification of sensorless control without compensation method is as follows: Figure 7 As shown, the estimated rotor position differs significantly from the actual position by a considerable angular difference, with an error range of 1.5° to 3.5°. The second operating condition verifies the use of a compensation method for sensorless control, as shown... Figure 8 As shown, the angle difference between the estimated rotor position and the actual position after compensation is reduced compared with that before compensation, with an error range of 2° to 3°, and the fluctuation range is reduced by 50%, which proves the effectiveness of the method of the present invention.

[0100] The method of this invention is designed for dual three-phase permanent magnet synchronous motors with asymmetrical inductance. While achieving sensorless control angle estimation, it identifies the asymmetrical inductance online and compensates for the identified inductance deviation in position demodulation, thereby reducing the error in the estimated angle and improving the performance of sensorless control.

[0101] The above description is merely a specific 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.

Claims

1. A sensorless control angle compensation method for a dual three-phase permanent magnet synchronous motor, characterized in that the steps are as follows: as follows: Step 1: Construct a mathematical model of a dual three-phase permanent magnet synchronous motor and derive the expression for the dq-axis inductance when the inductance is asymmetrical. Inject orthogonal square waves into the α-β axes of the stationary coordinate system, where dq and α-β are the coordinate systems obtained by rotating the natural coordinate system through Park and Clark transformations, respectively. The Park transformation is the coordinate transformation matrix from the stationary coordinate system to the rotating coordinate system, and the Clark transformation is the coordinate transformation matrix from the natural coordinate system to the stationary coordinate system. Sample the high-frequency current response four times during each square wave injection cycle. Construct an expression for the rotor position information using the sampled high-frequency response current values ​​and demodulate the rotor position angle. Step 2: Construct an expression for the dq inductance when the inductance is asymmetrical using the high-frequency response current sampling values, and identify the asymmetry. Inductance parameters It is an asymmetrical inductor along the d-axis. For q-axis asymmetric inductance; where I is constructed using sampled values. L0 and I L1 The specific construction process of the function is as follows: ； ； I L0 with I sinq I cosq The construction process is the same: at t=1, the current difference along the b-axis of the injected square wave response is selected at time t=1. Subtract the current difference along the a-axis of the injected square wave response at time t=4. At t=2, the current difference along the a-axis of the injected square wave response is selected at time t=2. Adding the current difference along the b-axis of the injected square wave response at time t=1 And so on; I L1 Then it is the constructed current I sinq I cosq The arithmetic square root of the sum of squares; Construct I L0 and I L1 The expression is: ； Identify through mathematical operations The inductance parameters are: ； Step 3: Based on the inductance identification results, calculate the deviation of the inductance asymmetry dq, and eliminate the deviation during position demodulation to improve the accuracy of rotor position estimation without position sensors; In step three, the asymmetry is calculated based on the inductance identification results. , Inductance deviation: ； In the formula, DL d and DL q The inductance deviation caused by asymmetry; the inductance deviation is removed from the position demodulation method. Mid-compensation, the expression after compensation H Dq for: ； Finally, the accurate rotor position angle is obtained through phase-locked loop processing. .

2. The sensorless control angle compensation method for dual three-phase permanent magnet synchronous motors as described in claim 1, characterized in that, In step one, the mathematical model of the dual three-phase permanent magnet synchronous motor is constructed as follows: ； In the formula, u dh u qh and u x u y These represent the high-frequency voltage signals injected along the d-axis and q-axis, and the xy harmonic subplane voltages, respectively; i dh i qh and i x i y These represent the d-axis and q-axis high-frequency current response components and the xy harmonic subplane currents, respectively; L d L q These are the high-frequency inductance values ​​for the d-axis and q-axis, respectively; L z For motor leakage inductance; The expression for the inductance dq when the inductance is asymmetrical is: ； In the formula, , dq is the inductance when the inductance is unbalanced; ΔL is the unbalanced inductance; θ is the rotor position angle. The orthogonal square wave voltage signal injected into the α-β axes of the stationary coordinate system without position sensor control is: ； In the formula, V h The value of the injected square wave is T; the period of the injected square wave is n; and the injection order is n. The expression for the sampled high-frequency response current is: ； In the formula, Δi αh and Δi βh The high-frequency current difference between two adjacent sampling points; L0 is the average inductance, L0 = (L d +L q ) / 2; L1 is the differential inductance, L1=(L d -L q ) / 2; t is the number of samples; By constructing a reasonable expression for θ based on the sampled values, the specific construction is as follows: ； ； Take I sinθ For example, in the construction: at t=1, the current difference Δi of the injected square wave response along the α axis is selected. αh t1 Subtract the current difference Δi along the β axis of the injected square wave response at time t=4. βh t4 ; At t=2, the current difference Δi in the β-axis of the injected square wave response is selected at time t=2. βh t2 Add the current difference Δi along the α axis of the injected square wave response at time t=1 αh t1 And so on, constructing I sinθ I cosθ The expression is: ； After rotor position demodulation, an expression for Δθ is obtained. for: ； In the formula, Δθ represents the difference between the actual rotor angle θ and the estimated rotor angle. The difference is due to inductance asymmetry, resulting in a deviation in the demodulation, leading to inaccurate position estimation. This is then processed by a phase-locked loop to obtain the rotor position angle. .

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