A fundamental and third harmonic current cooperative control method for permanent magnet synchronous motor

Abstract

The application provides a permanent magnet synchronous motor fundamental wave and third harmonic current collaborative control method, and belongs to the technical field of motor control. The method is driven by a three-phase four-bridge-arm inverter with a fourth bridge arm connected to the neutral point of the motor; the stator temperature, the rotating speed and the load torque are obtained; the fundamental wave and third harmonic permanent magnet fluxes with different temperature coefficients are calculated according to the temperature; the dynamic coupling coefficient composed of the product of the temperature compensation factor, the rotating speed and the load correction coefficient is calculated, the temperature compensation factor is the ratio of the flux ratio at the reference temperature to the current temperature; the ratio of the current margin to the fundamental wave current amplitude reference value is calculated, if the ratio is not greater than the threshold value, the injection is prohibited, otherwise the smaller value of the product of the theoretical optimal injection coefficient and the dynamic coupling coefficient and the ratio is taken as the optimal injection coefficient; the ratio of the third harmonic and the fundamental wave cross-axis current given value is equal to the optimal injection coefficient, the control quantity is combined through the double current loop control, and the inverter is driven by the three-dimensional space vector pulse width modulation.

Description

Technical Field

[0001] This invention belongs to the field of motor control technology, specifically relating to a method for coordinated control of the fundamental and third harmonic currents of a permanent magnet synchronous motor. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs), with their high power density, high efficiency, and excellent dynamic performance, are widely used in high-performance drive applications such as new energy vehicles, industrial robots, and aerospace. As the requirements for output torque density in these applications continue to increase, how to further improve the motor's torque output capability under limited stator current and voltage constraints has become a persistent concern in the field of motor drive control. Injecting third harmonic current into the stator windings is one of the effective technical means to improve the output torque density of PMSMs. Since the third harmonic current has the same phase in the three-phase windings and is a zero-sequence current, traditional three-phase three-wire three-arm inverters cannot provide a flow path for it. However, three-phase four-arm inverters, by adding a fourth arm and connecting the neutral point of the motor's three-phase windings to the midpoint of the fourth arm, can provide an independent flow path for the zero-sequence third harmonic current, thus becoming an ideal topology for third harmonic injection.

[0003] Currently, there are numerous publicly available technologies for increasing torque through third harmonic injection. For example, patent document CN122316158A discloses a technical solution for increasing the maximum output torque of a motor through third harmonic injection; patent documents CN121887041A and CN120262987B disclose a technical solution combining temperature compensation and harmonic current injection; and patent document CN114244215B discloses a technical solution for adjusting the harmonic injection amplitude according to the rotational speed. However, the aforementioned prior art still has the following shortcomings.

[0004] Firstly, existing third harmonic injection schemes typically employ fixed harmonic injection coefficients and fixed coupling coefficients to achieve torque distribution between the fundamental and harmonic frequencies. In actual operation of permanent magnet synchronous motors, the permanent magnet flux linkage decays with increasing temperature, and the decay characteristics of the fundamental flux linkage and the third harmonic flux linkage are not the same; the third harmonic flux linkage is more sensitive to temperature. When temperature changes, the fixed coupling coefficient cannot reflect the actual flux linkage ratio, leading to deviations in torque distribution and a significant decrease in torque enhancement as temperature rises.

[0005] Secondly, although some existing solutions have introduced the idea of ​​temperature-compensated flux linkage, the temperature compensation factor is canceled out in the final calculation of the injection coefficient, resulting in the final injection coefficient being completely unrelated to temperature. Temperature compensation cannot have a real impact on the torque boost effect, making it difficult to achieve a stable torque boost rate across the entire temperature range.

[0006] Third, existing technologies generally lack a systematic evaluation mechanism for current margin in harmonic injection decisions. When the motor is already close to its current limit, forcibly injecting harmonic current may cause the total current to exceed the controller's capacity limit, triggering overload protection or even damaging power devices. At the same time, if harmonic injection is directly implemented when the current margin is limited, it can easily cause torque fluctuations and operational instability.

[0007] Fourth, at the control level, existing fundamental and third harmonic current loops mostly use PI regulators, which have limited robustness to parameter perturbations and external disturbances. Furthermore, schemes employing active disturbance rejection control often lack specific details regarding the order of the extended state observer, the form of the nonlinear function, the combination of state error feedback methods, and the discretization implementation steps, making them difficult to reproduce in engineering. Simultaneously, for three-phase four-arm topologies, traditional two-level two-dimensional space vector modulation is no longer applicable, necessitating the use of three-dimensional space vector pulse width modulation.

[0008] Therefore, how to maintain a stable and near-optimal torque boost under temperature changes and different speeds and load conditions, how to reliably implement third harmonic injection while ensuring that the total current does not exceed the controller capacity and avoiding frequent switching, and how to provide a fundamental and third harmonic coordinated control scheme with a complete controller structure, engineering reproducibility, and matching with the three-phase four-arm hardware topology have become urgent technical problems to be solved in this field. Summary of the Invention

[0009] To address the shortcomings and deficiencies of existing technologies, this invention provides a method for the coordinated control of fundamental and third harmonic currents in a permanent magnet synchronous motor (PMSM). The PMSM is driven by a three-phase four-arm inverter, with the midpoint of the fourth arm connected to the neutral point of the three-phase windings, providing a flow path for the zero-sequence third harmonic current. This method acquires stator temperature, rotor electrical angular velocity, and load torque in each control cycle. Temperature compensation is applied to the fundamental and third harmonic permanent magnet flux linkages based on the stator temperature. The temperature coefficients of the two are different and both are negative, with the absolute value of the third harmonic flux linkage temperature coefficient being greater than that of the fundamental flux linkage. A dynamic coupling coefficient is calculated, consisting of the product of a temperature compensation factor, a speed correction factor, and a load correction factor. The temperature compensation factor is the ratio of the third harmonic flux linkage to the fundamental flux linkage at the reference temperature to the ratio of the temperature-compensated third harmonic flux linkage to the fundamental flux linkage at the current temperature, embedded as a multiplicative correction term. This ensures that temperature information is incorporated into the solution process. During the process, it is not canceled out; the current margin is calculated, and the third harmonic injection is prohibited when the ratio of the current margin to the reference value of the fundamental current amplitude is not greater than the preset threshold. Otherwise, it is enabled and the amplitude is limited cycle by cycle. Under the enabled condition, the smaller value between the theoretical optimal harmonic injection coefficient after dynamic coupling coefficient correction and the ratio is taken as the optimal harmonic injection coefficient. Based on this, the ratio of the third harmonic quadrature axis current setpoint to the fundamental quadrature axis current setpoint is determined. The fundamental current loop controller and the third harmonic current loop controller are controlled in concert. After the control quantities are combined, they are driven by three-dimensional space vector pulse width modulation to achieve stable torque boost rate under the full temperature range and different speed and load conditions.

[0010] The specific technical solution adopted by this invention to solve its technical problem is as follows:

[0011] This invention provides a method and system for coordinated control of the fundamental and third harmonic currents of a permanent magnet synchronous motor, in order to solve the problems in the prior art where the torque boost rate decreases with increasing temperature due to the fixed coupling coefficient, temperature compensation fails due to cancellation in algebraic operations, the lack of a current margin assessment mechanism leads to overcurrent risk and frequent switching, and the controller structure is difficult to reproduce in engineering.

[0012] A method for coordinated control of fundamental and third harmonic currents in a permanent magnet synchronous motor (PMSM), wherein the PMSM is driven by a three-phase four-arm inverter, the midpoint of the fourth arm of the inverter is connected to the neutral point of the three-phase windings of the motor, providing a flow path for the third harmonic zero-sequence current; the method includes the following in each control cycle:

[0013] Obtain the stator temperature, rotor electric angular velocity, and load torque of the permanent magnet synchronous motor.

[0014] Based on the stator temperature, the temperature-compensated fundamental and third harmonic permanent magnet flux linkages are calculated separately. The temperature coefficients of the fundamental and third harmonic flux linkages are different and both are negative, with the absolute value of the third harmonic flux linkage temperature coefficient being greater than that of the fundamental flux linkage. Both the fundamental and third harmonic flux linkages decrease with increasing temperature, and the third harmonic flux linkage is more sensitive to temperature. Since their decrease rates differ, they need to be compensated separately according to their respective temperature coefficients to reflect the true change in flux linkage ratio with temperature.

[0015] The dynamic coupling coefficient is calculated as the product of the temperature compensation factor, the speed correction factor, and the load correction factor. The temperature compensation factor is the ratio of the third harmonic permanent magnet flux linkage to the fundamental permanent magnet flux linkage at the reference temperature, and the ratio of the third harmonic permanent magnet flux linkage to the fundamental permanent magnet flux linkage after temperature compensation at the current temperature. By using this ratio, the temperature compensation factor is embedded as a multiplicative correction term into the dynamic coupling coefficient. The entire dynamic coupling coefficient serves as a correction factor for the theoretically optimal harmonic injection coefficient in subsequent solutions. Temperature information is not algebraically canceled during this solution process, thus allowing the optimal harmonic injection coefficient to adaptively change with temperature.

[0016] The current margin is calculated as the difference between the maximum allowable current of the controller and the current stator current amplitude. The ratio of the current margin to the reference value of the fundamental current amplitude is also calculated. Third harmonic injection is prohibited when this ratio is not greater than a preset threshold; otherwise, third harmonic injection is enabled, and the smaller of the product of the theoretically optimal harmonic injection coefficient and the dynamic coupling coefficient and this ratio is taken as the optimal harmonic injection coefficient. Taking the smaller value means choosing the smaller of the two values: when the current margin is sufficient, the injection coefficient is the result of the theoretically optimal value corrected by the dynamic coupling coefficient, achieving maximum torque enhancement; when the current margin is insufficient, the injection coefficient is automatically compressed to the physical limit corresponding to this ratio, ensuring that the total current does not exceed the limit. The preset threshold serves as the enable judgment criterion to avoid frequent switching of harmonic injection near the current margin threshold; as a preferred implementation, the preset threshold ranges from 0.02 to 0.10.

[0017] The ratio of the third harmonic quadrature-axis current setpoint to the fundamental quadrature-axis current setpoint is set to the optimal harmonic injection coefficient. The fundamental and third harmonic quadrature-axis current setpoints are input to the fundamental current loop controller and the third harmonic current loop controller, respectively. The control quantities of the two current loop controllers are combined after coordinate transformation, and a three-dimensional space vector pulse width modulation (SVM) is used to drive the three-phase four-arm inverter. The control quantity of the fundamental current loop is in the fundamental rotating coordinate system, the control quantity of the third harmonic current loop is in the third harmonic rotating coordinate system, and the three-dimensional space vector pulse width modulation is implemented in the abc coordinate system. Therefore, the control quantities need to be combined after coordinate transformation to form a reference voltage vector output to the three-phase four-arm inverter.

[0018] Furthermore, the speed correction coefficient is a piecewise function: when the absolute value of the rotor electrical angular velocity is greater than the speed correction threshold, the speed correction coefficient is the ratio of the speed correction threshold to the absolute value of the rotor electrical angular velocity; when the absolute value of the rotor electrical angular velocity is not greater than the speed correction threshold, the speed correction coefficient is equal to 1; the speed correction threshold is taken as 60% to 80% of the rated electrical angular velocity of the motor. In the high-speed range, the speed correction coefficient decreases inversely with the increase of speed, reducing the harmonic injection ratio and avoiding excessively high harmonic frequencies that lead to increased inverter switching losses and decreased current tracking performance; taking the absolute value form ensures that the coefficient is positive when the motor is in forward or reverse rotation.

[0019] Furthermore, the load correction factor is 1 plus the load influence factor multiplied by the ratio of load torque to rated torque, where the load influence factor ranges from 0.05 to 0.15. The load correction factor increases moderately with increasing load torque, improving the harmonic injection ratio under heavy load and fully utilizing the contribution of harmonic torque under high load conditions.

[0020] Furthermore, the theoretically optimal harmonic injection coefficient is set to 1 / 6. This value is determined based on the flat-top wave injection principle under peak current constraints: the phase current after injecting the third harmonic exhibits a flat-top wave shape, and the phase current peak value reaches its minimum when the theoretically optimal harmonic injection coefficient is set to 1 / 6. At this point, the phase current peak value drops to approximately 0.866 times that before injection. Under the constraint that the phase current peak value remains unchanged before and after harmonic injection, the fundamental current amplitude can be increased to 1.155 times, thereby obtaining a larger fundamental torque output space under the same current peak value.

[0021] Furthermore, the electromagnetic torque of the permanent magnet synchronous motor is the sum of the fundamental torque component and the third harmonic torque component. The product of the third harmonic permanent magnet flux linkage and the third harmonic cross-axis current in the third harmonic torque component is multiplied by a coefficient of 3. The ratio of the third harmonic torque to the fundamental torque is the product of the optimal harmonic injection coefficient, coefficient 3, and the ratio of the third harmonic permanent magnet flux linkage to the fundamental permanent magnet flux linkage at the current temperature. Coefficient 3 originates from the third harmonic flux linkage's time derivative generating a third-harmonic back electromotive force, and the zero-sequence third harmonic current's in-phase superposition in the three-phase windings, causing the three-phase power to act together on the electromagnetic torque. Because the optimal harmonic injection coefficient incorporates a temperature compensation factor, when the limiting function is not in effect, the current temperature flux linkage ratio and the temperature compensation factor in this torque ratio are exactly eliminated after algebraic operations. The ratio of the third harmonic torque to the fundamental torque remains a constant value independent of temperature, which is the mechanism for the stable torque boost rate across the entire temperature range. Considering that the current temperature flux ratio in the temperature compensation factor and the current temperature flux ratio in the torque ratio are mathematically reciprocals, this design allows the temperature compensation information to be naturally eliminated after the correction of the dynamic coupling coefficient is completed, rather than being lost meaninglessly during the calculation of the injection coefficient as in existing technologies.

[0022] Furthermore, both the fundamental current loop controller and the third harmonic current loop controller employ a nonlinear active disturbance rejection control structure, each including a tracking differentiator, a second-order nonlinear extended state observer, and a nonlinear state error feedback control law. The second-order nonlinear extended state observer expands the total disturbance into state variables, and calculates the observation error using a piecewise nonlinear function to estimate and compensate for the total disturbance. In the nonlinear state error feedback control law, the nonlinear factor corresponding to the tracking error is greater than 0 and less than 1, while the nonlinear factor corresponding to the differential error is greater than 1. The piecewise nonlinear function operates according to the power of the error and the sign of the error when the absolute value of the observation error is greater than the width of the linear interval, and operates in linear form when the absolute value of the observation error is not greater than the width of the linear interval. Based on the idea of ​​large error, small gain, and small error, large gain, the nonlinear factor corresponding to the tracking error is greater than 0 and less than 1, while the nonlinear factor corresponding to the differential error is greater than 1. The two work together to balance dynamic response and steady-state accuracy.

[0023] Furthermore, the second-order nonlinear extended state observer employs Euler's method for first-order forward differential discretization, where the update term of the total perturbation observation includes a nonlinear function value of the observation error, and this nonlinear function value is preceded by a negative sign. The gain of the second-order nonlinear extended state observer is tuned using the bandwidth method, and the observer bandwidth of the third harmonic current loop controller is taken as 1.2 to 2.0 times that of the observer bandwidth of the fundamental current loop controller. This negative sign is consistent with the sign of the continuous form, ensuring the convergence of the observer after discretization. The observer bandwidth of the third harmonic current loop is higher than that of the fundamental current loop to accommodate the higher frequency characteristics of the third harmonic component.

[0024] Furthermore, the load torque is extracted from the expanded state of the third-order nonlinear expanded state observer of the velocity outer loop after deducting the damping term and the mechanical angular velocity reduction term; or it is calculated according to the equation of motion based on the differentials of electromagnetic torque, moment of inertia, rotor mechanical angular velocity, and damping coefficient. The former method does not require additional differential calculations and has better noise immunity, while the latter method has a simpler structure. Both methods can obtain the load torque estimate in real time, providing input for the calculation of the dynamic coupling coefficient.

[0025] Furthermore, the three-dimensional spatial vector pulse width modulation is implemented in the abc coordinate system. The 16 switching states of the three-phase four-arm inverter correspond to 14 non-zero switching voltage vectors and 2 zero switching voltage vectors, forming a dodecahedron in three-dimensional space and dividing it into 24 spatial tetrahedrons. The spatial tetrahedron where the reference voltage vector is located is located by a pointer function, and the duty cycle is solved. The fundamental direct-axis current setpoint and the third harmonic direct-axis current setpoint are both set to zero. The pointer function is composed of judgment variables determined by the signs of each component of the reference voltage vector and the signs of their pairwise differences. Its value uniquely corresponds to the spatial tetrahedron where the reference voltage vector is located. Based on this, a table is consulted to determine the non-zero switching voltage vectors participating in the synthesis and to solve the duty cycle. The modulation process does not require coordinate transformation. The fundamental direct-axis current setpoint and the third harmonic direct-axis current setpoint are both set to zero, that is, a control strategy with zero direct-axis current is adopted.

[0026] This invention also provides a coordinated control system for the fundamental and third harmonic currents of a permanent magnet synchronous motor (PMSM), comprising a three-phase four-arm inverter, a surface-mounted PMSM, a temperature sensor, a current sensor, a position sensor, and a digital signal processor. The midpoints of the first three arms of the three-phase four-arm inverter are respectively connected to the three-phase windings of the surface-mounted PMSM, and the midpoint of the fourth arm is connected to the neutral point of the three-phase windings of the surface-mounted PMSM. A filter inductor is connected in series on the neutral line between the midpoint of the fourth arm and the neutral point. The digital signal processor stores a computer program, which, when executed, implements the above method. The filter inductor is used to suppress switching ripple on the neutral line, and the third harmonic zero-sequence current forms an independent flow loop with the fourth arm via the neutral line.

[0027] Compared to existing technologies, this invention and its preferred solution, through the embedding structure of the ratio of dual magnetic flux temperature compensation and temperature compensation factor, ensure that temperature information truly participates in the online solution of the optimal harmonic injection coefficient without being algebraically canceled. When the limiting function is not in effect, the ratio of third harmonic torque to fundamental torque remains constant, thus maintaining a stable torque boost effect across the entire temperature range. This overcomes the defect of the fixed coupling coefficient scheme where the torque boost rate decreases with increasing temperature. The dynamic coupling coefficient adopts a three-factor product structure of temperature, speed, and load, enabling the torque distribution ratio of the fundamental and third harmonics to be adaptively adjusted online according to operating conditions. The dual-layer current margin protection, consisting of enable threshold judgment and cycle-by-cycle limiting, avoids frequent switching at the current margin critical point and ensures that the total current does not exceed the limit; online optimization of the theoretical optimal value and the physical limit to take the minimum value, approximating the theoretical optimal value as much as possible under safety constraints; the fundamental and third harmonic dual current loop adopts a structurally complete, discretizable cycle-by-cycle nonlinear active disturbance rejection control, which is robust to parameter perturbations and external disturbances; the three-phase four-bridge-arm inverter and three-dimensional space vector pulse width modulation provide a clear flow path and modulation means for the zero-sequence third harmonic current, and the control method is consistent with the hardware topology. Attached Figure Description

[0028] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0029] Figure 1 This is an overall flowchart of the collaborative control method according to an embodiment of the present invention;

[0030] Figure 2 This is a schematic diagram illustrating the calculation of temperature compensation and dynamic coupling coefficient in an embodiment of the present invention;

[0031] Figure 3 This is a schematic diagram illustrating the dual-layer protection of current margin and online optimization of the optimal harmonic injection coefficient in an embodiment of the present invention.

[0032] Figure 4 This is a comparison chart showing the effect of temperature compensation on torque enhancement in an embodiment of the present invention. Detailed Implementation

[0033] To make the features and advantages of the present invention more apparent and understandable, specific embodiments are described below in detail:

[0034] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0035] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0036] This invention provides a third harmonic coordinated control method and system that can adaptively adjust the distribution of fundamental and third harmonic torques according to real-time operating conditions, has dual-layer protection with current margin, and has a fully disclosed controller structure that matches the hardware topology of a three-phase four-bridge.

[0037] The three-factor product dynamic coupling coefficient referred to in this invention is a dynamic coupling coefficient composed of the temperature compensation factor, the speed correction factor, and the load correction factor in a product structure, which is different from the fixed coupling coefficient in the prior art. The online optimization referred to in this invention means that within each control cycle, the optimal harmonic injection coefficient is solved online by combining the theoretically optimal injection coefficient corrected by the dynamic coupling coefficient with the physical current margin limit, and taking the minimum value, so that the injection amplitude always operates at the achievable optimal point under the current operating conditions.

[0038] like Figure 1 As shown, the collaborative control method of this invention is executed cycle by cycle according to the following link: First, operating parameters such as temperature, speed, and load torque are acquired; after calculation by the dual flux linkage temperature compensation model and the three-factor product dynamic coupling coefficient, it enters the current margin double-layer protection loop; under the enabled condition, the optimal harmonic injection coefficient is solved online according to the method of taking the minimum value of theoretical optimal and physical limit; then, torque distribution is performed and the fundamental and third harmonic dual NLADRC (nonlinear active disturbance rejection control) current loop is coordinated and controlled; finally, the three-phase four-arm inverter is driven by 3D-SVPWM (three-dimensional space vector pulse width modulation).

[0039] The collaborative control method of the present invention includes the following steps.

[0040] Step 1: Obtain real-time operating parameters of the permanent magnet synchronous motor, including the motor stator temperature. Rotor electric angular velocity and load torque The load torque is obtained in real time through estimation.

[0041] Step 2: Establish a dual flux linkage temperature compensation model, and calculate the fundamental permanent magnet flux linkage after temperature compensation based on the stator temperature. and third harmonic permanent magnet flux The temperature coefficients of the fundamental permanent magnet flux linkage and the third harmonic permanent magnet flux linkage are different.

[0042] Step 3, calculate the dynamic coupling coefficient. The dynamic coupling coefficient is the product of the temperature compensation factor, the speed correction factor, and the load correction factor, and is used to determine the torque distribution ratio between the fundamental wave and the third harmonic.

[0043] Step 4: Implement dual-layer current margin protection. The first layer is the enable threshold judgment, and the second layer is cycle-by-cycle limiting.

[0044] Step 5: Under the condition of enabling third harmonic injection, solve the optimal harmonic injection coefficient online by combining the theoretical optimal value with the physical limiting method. .

[0045] Step 6: Distribute torque according to the optimal harmonic injection coefficient and calculate the fundamental quadrature-axis current setpoint. and the third harmonic quadrature-axis current setpoint The fundamental current loop nonlinear active disturbance rejection controller and the third harmonic current loop nonlinear active disturbance rejection controller are respectively input to achieve coordinated control of the fundamental and third harmonic dual current loops.

[0046] Step 7: After coordinate transformation, the control quantities of the fundamental current loop and the third harmonic current loop are merged, and a three-dimensional space vector pulse width modulation strategy is used to drive the three-phase four-arm inverter to control the operation of the permanent magnet synchronous motor. The midpoints of the first three arms of the three-phase four-arm inverter are connected to the three-phase windings of the permanent magnet synchronous motor, respectively. The midpoint of the fourth arm is connected to the neutral point of the three-phase windings of the permanent magnet synchronous motor. The third harmonic current has the same phase in the three-phase windings and is a zero-sequence current, forming a current loop through the fourth arm.

[0047] The system of this invention includes a three-phase four-arm inverter, a surface-mount permanent magnet synchronous motor, a temperature sensor, a current sensor, a position sensor, and a digital signal processor. The midpoints of the first three arms of the three-phase four-arm inverter are respectively connected to the three-phase windings of the surface-mount permanent magnet synchronous motor, and the midpoint of the fourth arm is connected to the neutral point of the three-phase windings of the motor. A filter inductor is connected in series on the neutral line between the midpoint of the fourth arm and the neutral point. The digital signal processor stores a computer program, which, when executed, implements the aforementioned coordinated control method.

[0048] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings:

[0049] 1. System hardware topology and zero-sequence current flow loop

[0050] A three-phase four-arm inverter consists of four arms and a total of eight power switching transistors. The first three arms are responsible for outputting the three-phase current from the inverter, with their midpoints connected to the A, B, and C phase windings of a surface-mounted permanent magnet synchronous motor, respectively. The midpoint of the fourth arm is connected to the neutral point of the motor's three-phase windings, and a filter inductor is connected in series on the neutral line between the midpoint of the fourth arm and the neutral point to suppress switching ripple. Due to the presence of the fourth arm, the inverter introduces an additional degree of freedom, allowing control of the neutral point voltage. Regardless of whether the load is unbalanced, it can output symmetrical three-phase voltages.

[0051] The third harmonic current is in phase in the three-phase windings, and the three-phase third harmonic components are superimposed in phase, belonging to the zero-sequence current. In a traditional three-phase three-wire three-arm inverter, the zero-sequence current has no flow path; however, in the three-phase four-arm topology of this invention, the zero-sequence third harmonic current flows from the three-phase windings into the neutral point, through the neutral line and the filter inductor to the midpoint of the fourth arm, where the upper and lower power switches of the fourth arm form a freewheeling loop, thus providing an independent flow path for the third harmonic current. This is the topological basis for the hardware implementation of third harmonic injection, and the control method is strictly self-consistent with the hardware topology.

[0052] A temperature sensor is used to collect the motor temperature. Preferably, an NTC thermistor or thermocouple embedded in the stator winding can be used. The temperature sampling period is synchronized with or an integer multiple of the current control period. A current sensor is used to collect the three-phase stator current. A Hall effect current sensor can be used, and the data is sent to a digital signal processor via an ADC interface. A position sensor is used to collect the rotor position and speed. A rotary transformer can be used. The digital signal processor can be a 32-bit floating-point digital signal processor, which completes all online calculations of the method of this invention within one current control cycle. The total computational load of the method of this invention within one control cycle is comparable to that of conventional vector control. The digital signal processor can execute the calculations cycle by cycle in real time at a 10kHz switching frequency.

[0053] To achieve closed-loop control of the fundamental and third harmonic components, the system synchronously samples the three-phase current at high speed and separates the fundamental and third harmonic components in real time using a phase-locked loop. The fundamental d-axis and q-axis currents are then obtained through coordinate transformation. , and third harmonic d-axis and q-axis currents , Four feedback components serve as feedback inputs for the four current channels.

[0054] 2. Real-time acquisition of operating parameters and online estimation of load torque

[0055] Temperature is acquired via a temperature sensor. Rotor position is obtained by a position sensor, and rotor electrical angular velocity is calculated from rotor position using differentiation. Load torque is obtained in real time through estimation; this invention provides the following two methods.

[0056] Method 1: Extraction of the extended state using a third-order nonlinear extended state observer of the velocity outer loop. The motor motion equations are as follows:

[0057]

[0058] in, For rotational inertia, Let be the rotor's mechanical angular velocity, and , This represents the number of pole pairs of the motor. Let be the damping coefficient. The equations of motion are rearranged into second-order equations concerning the rotor position (electric angle).

[0059]

[0060] in, For rotor electrical angle, The speed loop control gain (its expression is shown in equation (2)). The reference value for the q-axis current output by the outer velocity loop is given by the formula. Parameter perturbations are also included in the total disturbance. The outer velocity loop employs a second-order nonlinear active disturbance rejection control structure, configured with a third-order nonlinear extended state observer, wherein... Observe the rotor position. Observe rotational speed and expansion state The total disturbance is estimated in real time, and its continuity equation is:

[0061] (1)

[0062] In the formula For position observation error, , , For the velocity loop observer gain, For nonlinear interval range parameters, It is a nonlinear function, and its expression is shown in equation (22). The speed loop control gain is determined by the following formula:

[0063] (2)

[0064] In the formula The fundamental permanent magnet flux linkage after temperature compensation is expressed in equation (5). In the derivation of equation (2), the electromagnetic torque is mainly based on the fundamental component. As a preferred implementation, the velocity loop observer gain can be determined by referring to the bandwidth method based on the velocity loop observer bandwidth. Adjustment, take , , The linearized observer characteristic polynomial is The velocity loop observer uses a linear error term in the first row to simplify calculations; as an equivalent replacement, a nonlinear function can also be used uniformly. In the form of.

[0065] From the expansion state For the estimated structure of the total disturbance, based on the total disturbance structure determined by the motor motion equations, the estimated load torque value is:

[0066] (3)

[0067] That is, from the expansion state After deducting the damping term and the mechanical angular velocity conversion term, the load torque is extracted, where... This is the estimated value of the load torque.

[0068] Method 2, the equation of motion method, directly calculates based on the differential of electromagnetic torque and rotational speed:

[0069] (4)

[0070] in The electromagnetic torque is calculated from the current and temperature-compensated flux linkage according to equation (17) below. The differential rotational speed can be obtained by differential analysis and low-pass filtering of the position sensor signal. Method 1 does not require additional differential calculation and has better noise immunity, and is therefore the preferred embodiment of the present invention; Method 2 has a simple structure and is therefore an alternative.

[0071] 3. Dynamic coupling coefficient between the dual magnetic flux temperature compensation model and the three-factor product

[0072] Both the fundamental permanent magnet flux and the third harmonic permanent magnet flux decrease with increasing temperature, but their temperature coefficients are not the same. They are calculated separately using the following dual flux temperature compensation model:

[0073] (5)

[0074] (6)

[0075] in, , Reference temperature The fundamental permanent magnet flux linkage and the third harmonic permanent magnet flux linkage; The fundamental flux linkage temperature coefficient, Let be the temperature coefficient of the third harmonic flux linkage, and satisfy . This means that the third harmonic flux linkage is more sensitive to temperature than the fundamental flux linkage, which is consistent with the physical fact that the attenuation characteristics of the fundamental and third harmonic flux linkages are not entirely the same; reference temperature The preferred temperature is 25°C. For neodymium iron boron permanent magnet materials, The typical range of values ​​is / °C to / °C, The typical range of values ​​is / °C to / °C.

[0076] Dynamic coupling coefficient Temperature compensation factor Speed ​​correction coefficient With load correction factor The product of the three:

[0077] (7)

[0078] The temperature compensation factor is:

[0079] (8)

[0080] That is, the flux ratio at the reference temperature magnetic flux ratio at current temperature The ratio. When hour The greater the temperature deviates from the reference temperature, The greater the deviation from 1, the more accurately temperature information is embedded in the solution chain of the injection coefficients.

[0081] The speed correction factor is a piecewise function:

[0082] (9)

[0083] in The rated electrical angular velocity of the motor is used as the speed correction threshold. The harmonic injection ratio is 60% to 80%, preferably 70%. The speed correction factor is used to reduce the harmonic injection ratio during high-speed operation, avoiding excessively high harmonic frequencies that lead to increased inverter switching losses and decreased current tracking performance.

[0084] The load correction factor is:

[0085] (10)

[0086] in This is the load impact factor, typically ranging from 0.05 to 0.15, with 0.10 being preferred. This represents the rated torque of the motor. The load correction factor is used to appropriately increase the harmonic injection ratio under heavy load conditions, making full use of the contribution of harmonic torque under high load conditions.

[0087] It should be noted that the embedded structure of the temperature compensation factor ensures that the dynamic coupling coefficient is optimized in the online solution of equation (15) in subsequent step 5. The overall value is considered as the theoretically optimal injection coefficient. The correction factor is used in the calculation, temperature term It will not be cancelled out, thus achieving the optimal harmonic injection coefficient. It truly adapts to temperature changes, overcoming the limitation of existing schemes where temperature compensation is mathematically canceled out. Its effectiveness can be verified by the constant proportion of harmonic torque. Let the flux linkage ratio at the current temperature be... The flux ratio at the reference temperature is When the limiting factor is not in effect Then the ratio of the third harmonic torque to the fundamental torque is:

[0088] (11)

[0089] in , These are the third harmonic torque component and the fundamental torque component, respectively, and their expressions are shown in equation (17). The optimal harmonic injection coefficient; The theoretically optimal harmonic injection coefficient is taken as 1 / 6, the theoretical basis of which is shown in equation (14). That is, when the limiting term is not in effect, the proportion of harmonic torque is constant. It does not drift with temperature; while in the scheme using a fixed coupling coefficient, this proportion is... ,in For fixed harmonic injection coefficients that do not change with temperature, as The torque decreases due to attenuation. This is precisely the mechanism by which the torque boost rate remains stable across the entire temperature range in this invention. See also Figure 2 .

[0090] 4. Double-layer current margin protection and online optimization of optimal harmonic injection coefficient

[0091] Calculate the current margin:

[0092] (12)

[0093] in For current margin, The maximum allowable output current of the controller is determined by the current rating of the power devices and heat dissipation conditions, typically taken as 1.5 to 2.0 times the rated current of the motor. This represents the current amplitude of the stator current.

[0094] The first layer of protection uses an enable threshold for judgment. Only when... Enables third harmonic injection, in which This is a reference value for the fundamental current amplitude. The preset threshold value ranges from 0.02 to 0.10, with 0.05 being preferred. Third harmonic injection is enabled only when the current margin reaches 2% to 10% or more of the fundamental current amplitude reference value, in order to avoid frequent switching of third harmonic injection when the current margin is insufficient.

[0095] The second layer of protection is cycle-by-cycle limiting. Within each control cycle after enabling third harmonic injection, the optimal harmonic injection coefficient is limited to no more than [value missing]. This cycle-by-cycle limiting is derived from the following constraint: since the fundamental cross-axis current does not exceed its amplitude reference value, the third harmonic cross-axis current... To ensure that the total current after the third harmonic injection does not exceed the maximum allowable current of the controller, the following requirements must be met:

[0096] (13)

[0097] This allows for cycle-by-cycle limiting of the third harmonic injection amplitude within each control cycle. Even if the current margin suddenly decreases after the third harmonic injection is enabled, the third harmonic injection amplitude can be compressed in a timely manner to ensure that the total current does not exceed the limit.

[0098] Theoretically optimal harmonic injection coefficient is taken Its theoretical basis is the flat-top wave injection principle under peak current constraint. The phase current after injecting the third harmonic is expressed as:

[0099] (14)

[0100] in To inject the amplitude of the preceding phase current for harmonics, For electrical angle, Let be the harmonic injection coefficient. The above equation utilizes an identity. .when When, the above expression becomes The phase current waveform exhibits a flat-topped wave shape; for Finding the extreme value reveals that when The peak value of the phase current reaches its minimum value, which is approximately [value missing]. Therefore, under the constraint that the peak phase current remains unchanged before and after harmonic injection, the fundamental current amplitude can be increased to [value missing]. This corresponds to a theoretical fundamental torque increase of approximately 15.5%, therefore we take... .

[0101] Under the condition of third harmonic injection enablement, the optimal harmonic injection coefficient is solved online by combining the theoretical optimal value with the physical limiting method. :

[0102] (15)

[0103] in This represents the theoretically optimal harmonic injection coefficient. The structure, which combines this theoretically optimal value with the physical minimum limit, ensures that when the current margin is sufficient, the injection coefficient is the theoretically optimal value adjusted for operating conditions, achieving maximum torque enhancement; when the current margin is insufficient, the injection coefficient is automatically compressed to the physical limit, balancing torque enhancement and current constraint. See also... Figure 3 .

[0104] 5. Torque Distribution and Electromagnetic Torque Model

[0105] Fundamental quadrature-axis current setpoint The third harmonic quadrature-axis current setpoint, determined by the speed outer loop controller or external torque reference, is calculated as follows:

[0106] (16)

[0107] in This is the setpoint for the third harmonic quadrature-axis current. The setpoint for the fundamental direct-axis current. With the given value of the third harmonic direct-axis current All are set to 0, i.e., use Control strategy. and By inputting the fundamental current loop nonlinear active disturbance rejection controller and the third harmonic current loop nonlinear active disturbance rejection controller respectively, the coordinated control of the fundamental and third harmonic dual current loops can be achieved.

[0108] Electromagnetic torque is generated by the fundamental wave and the third harmonic, and its expression is:

[0109] (17)

[0110] in This represents the number of pole pairs of the motor. , These are the actual values ​​of the fundamental cross-axis current and the third harmonic cross-axis current, respectively. The factor 3 before the third harmonic torque term in the formula comes from two aspects. First, the third harmonic flux linkage... The amplitude of the back electromotive force obtained by differentiating with respect to time is Firstly, this factor naturally appears in the power balance derivation; secondly, the third harmonic currents are superimposed in phase in the three-phase windings, belonging to zero-sequence currents, and the superimposed three-phase power together acts on the electromagnetic torque. Therefore, the ratio of the third harmonic torque to the fundamental torque is... This is consistent with the analysis of the constant proportion of harmonic torque in the aforementioned equation (11).

[0111] 6. Design of dual nonlinear self-rejection current loop

[0112] The controlled object of the fundamental current loop is a first-order current equation. In the d1-q1 rotating coordinate system, the surface-mounted permanent magnet synchronous motor (… The fundamental voltage equation of () is rewritten as:

[0113] (18)

[0114] in , These are the fundamental direct-axis and quadrature-axis inductors, respectively. Let be the stator resistance. Let the fundamental frequency d-axis and q-axis control gain be denoted as . , The terms within the parentheses, excluding the control variables, are respectively assigned to the total disturbances along the fundamental d-axis and q-axis. , This includes internal and external disturbances such as cross-coupling terms, resistance voltage drop, back electromotive force, and temperature-induced flux drift.

[0115] The controlled object of the third harmonic current loop also follows a first-order current equation. The electrical angle of the third harmonic is three times that of the fundamental wave. After a d³-q³ coordinate transformation, the third harmonic voltage equation is rewritten as:

[0116] (19)

[0117] in , These are the average values ​​of the self-inductance and mutual inductance of the third harmonic stator, respectively. This is the fundamental electrical angle. Unlike the fundamental positive-sequence component, the third harmonic component is of zero-sequence nature, and its magnetic field is a pulsating magnetic field rather than a rotating magnetic field. Therefore, after the d3-q3 coordinate transformation, the following appears... , The time-varying back electromotive force term in the form of a third harmonic. Let the d-axis and q-axis control gain of the third harmonic be denoted. The terms within the square brackets are respectively attributed to the total disturbances along the d-axis and q-axis of the third harmonic. , The model uncertainties and unmodeled dynamics in the controlled object model are all included in the total disturbance, which is estimated and compensated online by the extended state observer. Therefore, the model accuracy does not affect the feasibility and effectiveness of the control method.

[0118] Since the controlled object is first-order, both the fundamental current loop and the third harmonic current loop adopt a first-order nonlinear active disturbance rejection control structure, each consisting of three parts: a tracking differentiator, a second-order nonlinear extended state observer, and a nonlinear state error feedback control law. The tracking differentiator, extended state observer, and error feedback control law of the two current loops operate independently. Each of the four current channels (fundamental d-axis, fundamental q-axis, third harmonic d-axis, and third harmonic q-axis) is configured with one of the above structures, and the variables and parameters in the formula are distinguished by adding axial subscripts d1, q1, d3, and q3 respectively.

[0119] The tracking differentiator tracks the current setpoint and provides an approximate differential signal, thus softening the start-up process. Taking the fundamental q-axis as an example, the continuous form of the tracking differentiator is:

[0120] (20)

[0121] in For a given value The tracking signal, when close enough hour, It can be regarded as an approximate differential signal of a given value. As the velocity factor, the tracking velocity and Proportional. The given value of the third harmonic q-axis tracking differentiator. This reflects the coupling relationship between the harmonic cross-axis current reference and the fundamental cross-axis current reference, i.e., the output of the torque distributor.

[0122] The second-order nonlinear extended state observer expands the total disturbance of a first-order system into new state variables, thus elevating it to second-order. Observe the actual value of the current. The continuity equation for the observed total disturbance is:

[0123] (twenty one)

[0124] in The actual current of the corresponding channel ( , , or ), For the observed value of the actual current, To the total disturbance of the corresponding channel ( , , or ) observations, For the control quantity of the corresponding channel ( , , or ), For the control gain of the corresponding channel, , For observer gain, , It is a nonlinear factor. This is a parameter for the nonlinear interval range.

[0125] nonlinear functions The expression is:

[0126] (twenty two)

[0127] in The error between the observed value and the actual value. For nonlinear factors, satisfying , The width of the linear interval. Nonlinear factor. Values ​​such as 0.5 and 0.25 are acceptable, as are values ​​other than 0.25 and 0.5. The smaller the value, the stronger the nonlinearity. To control the range of the linear interval, we usually set... ,in To control the cycle.

[0128] The nonlinear state error feedback control law performs a first nonlinear combination on the error between the tracking value of the tracking differentiator and the observation value of the extended state observer, and calculates the uncompensated control quantity:

[0129] (twenty three)

[0130] in To track the error of the observed value (e.g.) ), To track the error of the differential with respect to the observed differential, , For the control law gain, , As a nonlinear factor, it satisfies the principle of large error, small gain, and small error, large gain. Typical , , This is a parameter for the nonlinear interval range, typically taken as 0.01. (During engineering debugging...) Values ​​in the range of 500 to 40000 generally exhibit good convergence characteristics. Take a smaller value and adjust it in conjunction with the observer parameters.

[0131] Finally, the control input is generated according to the disturbance compensation method:

[0132] (twenty four)

[0133] in The final control value for the corresponding channel is given. This represents the total disturbance observation value updated for the current control cycle. Specifically, a compensation term is constructed using the observation value of the total disturbance from the extended state observer to offset the total disturbance, compensating each current channel as a standard integrator series configuration.

[0134] The observer and control law are discretized using the Euler method in each control cycle and executed cycle by cycle. The discretization equation of the second-order nonlinear extended state observer is as follows:

[0135] (25)

[0136] in To control the cycle, i.e. the integral step size, This is the control cycle number. Within each control cycle, the following steps are executed sequentially. First, the actual current of the four channels is sampled and separated. , , , Then, the observation error was calculated for each channel. Then update each channel according to formula (25). and Then calculate the tracking error for each channel. With differential error The uncompensated control quantity is calculated in the discrete form of equation (23). Then, the control values ​​for each channel are generated according to formula (24). , , , Finally, the control quantities are transformed into a reference voltage vector through coordinate transformation and then sent to the three-dimensional space vector pulse width modulation module.

[0137] As a preferred implementation, the tracking differentiator is implemented using a discrete steepest synthesis function (fhan) to balance tracking speed and noise suppression. Taking the fundamental q-axis as an example, the recursive form of the discrete steepest synthesis function is:

[0138] (26)

[0139] in The filter factor is typically taken as the control period. 1 to 5 times, The larger the value, the stronger the noise suppression and the greater the phase lag. For the speed factor, the same logic applies to the other channels. During tuning, first fix the filter factor at a small value, then adjust the speed factor by orders of magnitude until fast tracking without overshoot is achieved. Then, gradually increase the filter factor to suppress noise without sacrificing dynamic response.

[0140] The observer gain can be independently tuned using the bandwidth method. As a preferred implementation, for a second-order nonlinear extended state observer, its characteristic polynomial is set to [equation missing] under the linearization equivalence condition. , can be obtained , ,in Let the bandwidth of the observer be denoted as . Let the bandwidth of the fundamental current loop observer be denoted as . The bandwidth of the third harmonic current loop observer is To accommodate the higher frequency characteristics of the third harmonic component, the bandwidth of the third harmonic current loop observer is taken to be 1.2 to 2.0 times that of the fundamental current loop observer, i.e.

[0141] (27)

[0142] For example, it is advisable rad / s rad / s. The tuning principle is to first place the gain at a small value within the stable region, and then gradually increase it until the observation error converges rapidly and no oscillations occur. It mainly affects the convergence speed of the observer. The main impact is on convergence accuracy. A larger observer bandwidth results in faster perturbation estimation, but excessive bandwidth can introduce noise or even oscillations. The nonlinear state error feedback control law and the extended state observer parameters need to be adjusted in tandem to balance convergence speed and noise immunity. The observer gain should be tuned within the Euler discretization stability region, that is, under the linearization equivalent condition, the roots of the discrete observer characteristic equation should lie within the unit circle.

[0143] 7. Three-dimensional spatial vector pulse width modulation strategy

[0144] The control quantities of the fundamental and third harmonic current loops are combined into a reference voltage vector after coordinate transformation. A three-dimensional spatial vector pulse width modulation (SVPWM) strategy in the abc coordinate system is used to drive the three-phase four-arm inverter. This modulation algorithm does not require Clark transformation or its inverse transformation. The four arms of the three-phase four-arm inverter have a total of... There are 16 switching states, corresponding to 14 non-zero switching voltage vectors and 2 zero switching voltage vectors. These 16 switching voltage vectors form a closed dodecahedron in three-dimensional space. The dodecahedron is divided into 24 spatial tetrahedrons, each of which consists of 3 non-zero switching voltage vectors and 2 zero switching voltage vectors.

[0145] According to the reference voltage vector , , The sign of the and the sign of each pairwise difference define 6 judgment variables. ( ), and substitute the pointer function:

[0146] (28)

[0147] in This is the value of a pointer function. Derived from a pointer function. The value of determines the spatial tetrahedron where the reference voltage vector is located, and then the three non-zero switching voltage vectors participating in the synthesis are determined by looking up a table. The duty cycle of each non-zero switching voltage vector is obtained by solving the duty cycle matrix equation:

[0148] (29)

[0149] in , , These represent the duty cycles of the three non-zero switching voltage vectors involved in the synthesis. , , The three non-zero switching voltage vectors involved in the synthesis, determined by looking up a table, have subscripts a, b, and c indicating their components on the three-phase axes a, b, and c. , , Let be the three-phase reference voltage in the abc coordinate system. The duty cycle of the zero-switching voltage vector is .

[0150] (30)

[0151] in The duty cycle of the zero-switching voltage vector is given by the duty cycle of the two zero-switching voltage vectors. The switching is configured in a specific manner. During the switching process, only one bridge arm is changed at a time to reduce switching losses and voltage fluctuations. The filter inductor connected in series on the neutral line between the fourth bridge arm and the neutral point of the motor's three-phase windings is used to suppress switching ripple.

[0152] 8. Implementation Examples and Multi-Temperature Point Validation

[0153] Example 1 uses a 2kW surface-mounted permanent magnet synchronous motor as an example to present the complete implementation process and numerical examples of the cooperative control method. The motor parameters are: fundamental permanent magnet flux linkage. Wb (reference temperature) °C), third harmonic permanent magnet flux Wb, stator resistance Direct-axis inductor quadrature axis inductor H, the number of pole pairs .

[0154] In step 1, the motor temperature is acquired using an NTC thermistor with a sampling resolution of 12 bits, and the sampling period is synchronized with the current control period; the rotor position is obtained through a rotary transformer, and the electrical angular velocity is calculated by differentiation; the load torque estimate is obtained from the extended state of the third-order nonlinear extended state observer of the outer velocity loop. Extract according to formula (3).

[0155] In step 2, the parameters of the dual flux linkage temperature compensation model are taken as follows: / °C、 / °C. When the temperature rises from the reference temperature of 25°C to 100°C... Wb (attenuation of approximately 9%) Wb (attenuation of approximately 6%). It can be seen that the attenuation amplitude of the third harmonic flux linkage is greater than that of the fundamental flux linkage, and their attenuation characteristics are not the same.

[0156] In step 3, the rotational speed correction threshold is taken. ( (Rated electric angular velocity), load influence factor The flux linkage ratio was calculated at the reference temperature. At 100°C Temperature compensation factor Assume the motor is operating below its rated speed ( , ), rated load ( , Then the dynamic coupling coefficient .

[0157] In step 4, a preset threshold is taken. Reference value of fundamental current amplitude A, then only if Enable third harmonic injection at time A; upper current limit. The value is determined by the rated value of the controller's power devices, typically 1.5 to 2.0 times the rated current of the motor.

[0158] In step 5, the optimal harmonic injection coefficient is solved online according to equation (15), and the results are explained in three typical operating conditions.

[0159] Operating Condition 1 (Sufficient Margin) A, , This means the harmonic injection ratio is 18.9%. For comparison, under the 25°C reference operating condition... , , It can be seen that as the temperature increases, the temperature compensation factor... Increasing the injection ratio from 0.183 to 0.189 precisely offsets the additional attenuation of the third harmonic flux linkage, and temperature information is accurately incorporated into the online solution. At this point, the proportion of harmonic torque... The value is exactly the same as that at 25°C and does not drift with temperature.

[0160] Operating Condition 2 (Limited Margin) A, , The second layer of cycle-by-cycle amplitude limiting takes effect, and the harmonic injection amplitude is automatically compressed as the margin decreases, ensuring that the total current does not exceed the limit.

[0161] Operating condition 3 (insufficient margin). A, the enable criterion is not met. Third harmonic injection is prohibited. All current capacity is prioritized to ensure the fundamental torque output, while avoiding frequent switching near the critical point.

[0162] In step 6, the speed outer loop output is set. A, then working condition one A. The electromagnetic torque is calculated according to equation (17). N·m, of which the fundamental component contributes 4.484 N·m and the third harmonic component contributes 0.308 N·m, with the harmonic torque accounting for [percentage missing]. , with the above This aligns with the theoretical proportion.

[0163] In step 7, the first-order nonlinear active disturbance rejection controllers for the fundamental loop and the third harmonic loop are constructed according to equations (20) to (26), and are executed cycle-by-cycle according to equations (24) and (25), with the control cycle being... s, corresponding to a 10kHz switching frequency. The observer bandwidth is taken as... rad / s rad / s ); function parameter taking , , ;Parameter selection for nonlinear state error feedback control law , , , Adjust within the range of 500 to 40000 Take a smaller value and adjust the observer parameters accordingly. The control values ​​of the four channels are combined into a reference voltage vector through coordinate transformation. The duty cycle is calculated by the three-dimensional space vector pulse width modulation of the abc coordinate system according to equations (28) to (30) and the PWM signal is output to drive the three-phase four-arm inverter.

[0164] Example 2 compares the torque increase rate at five temperature points within the range of 25°C to 125°C using the fixed coupling coefficient scheme and the dynamic coupling coefficient scheme of this invention, under the motor and parameters described in Example 1. For ease of comparison, the torque increase rate is defined as the percentage increase in electromagnetic torque after injecting harmonic current relative to the case without injection (same fundamental current), and its value is equal to the ratio of harmonic torque to fundamental torque. The fixed coupling coefficient scheme has no temperature compensation, and the coupling coefficient is always set according to the flux linkage ratio at 25°C, that is, the injection coefficient is fixed at [value missing]. Its harmonic torque accounts for 1 / 3 of the total. The temperature compensation factor decreases as temperature increases; in the dynamic coupling coefficient scheme of this invention, the injection coefficient is adjusted online with temperature, and the proportion of harmonic torque remains constant. The calculation results are shown in the table below.

[0165]

[0166] At a reference temperature of 25°C, both schemes showed a torque increase rate of 6.89%. As temperature increased, in the fixed coupling coefficient scheme, the third harmonic flux decayed faster than the fundamental flux, and the flux ratio... The harmonic torque decreased from 0.12528 to 0.11984 (a relative decrease of approximately 4.3%), while the injection coefficient remained constant, and the proportion of harmonic torque... As the temperature decreases, the torque increase rate continuously drops from 6.89% to 6.59% at 125°C, a cumulative decrease of 0.30 percentage points; in the scheme of this invention, the temperature compensation factor... It increases with increasing temperature (e.g., at 100°C) This allows the injection coefficient to be adaptively adjusted online, while the proportion of harmonic torque remains constant. The torque boost rate remains constant at 6.89% across the entire temperature range, and at 125°C, it is 0.30 percentage points higher than the fixed coupling coefficient scheme, representing a relative improvement of approximately 4.6%. The temperature attenuation of the harmonic torque proportion is directly proportional to the difference in temperature coefficients between the fundamental and third harmonic flux linkages. The more significant the difference, the more pronounced the attenuation in the fixed scheme, while the scheme of this invention can completely offset these differences through a temperature compensation factor. It should be noted that the above torque boost rate corresponds to the actual torque gain of closed-loop injection under the same fundamental current; under extreme operating conditions where peak current is limited, the flat-top wave injection principle also provides approximately 15.5% more fundamental current boost space. The two methods have different scopes and do not conflict with each other. See [link to relevant documentation]. Figure 4 .

[0167] Comparative data at multiple temperature points show that the dynamic coupling coefficient scheme maintains a constant torque boost rate across the entire temperature range.

[0168] In summary, compared with the prior art, the technical advantages of this invention include:

[0169] By incorporating a dual-flux temperature compensation model and an embedded structure of temperature compensation factors, temperature information is accurately involved in the online solution of the optimal harmonic injection coefficient without being canceled out. This ensures that the proportion of harmonic torque remains constant and does not drift with temperature, thus guaranteeing a stable torque boost rate across the entire temperature range. This overcomes the defect of the fixed coupling coefficient scheme where the torque boost rate decreases with increasing temperature.

[0170] The dynamic coupling coefficient adopts a three-factor product structure of temperature compensation factor, speed derating correction and load derating correction, so that the torque distribution ratio of the fundamental wave and the third harmonic can be adaptively adjusted online according to temperature, speed and load conditions, and always approach the optimal operating condition.

[0171] The dual-layer current margin protection, consisting of enable threshold judgment and cycle-by-cycle limiting, prevents frequent switching of harmonic injection when the current margin is insufficient, and prevents the total current from exceeding the limit in each control cycle, thereby improving the safety and reliability of system operation.

[0172] The online solution structure, which integrates the theoretical optimal value and the physical minimum limit, allows the harmonic injection amplitude to be balanced between the theoretical optimal value and the current constraint online, while maximizing torque enhancement and achieving physical feasibility.

[0173] The fundamental and third harmonic dual nonlinear self-rejecting current loop structure is complete and can be discretized and implemented cycle by cycle, exhibiting strong robustness to parameter perturbations and external disturbances. The three-phase four-bridge inverter and three-dimensional space vector pulse width modulation provide a clear hardware flow loop and modulation means for the zero-sequence third harmonic current. The control method and hardware topology are strictly self-consistent, and those skilled in the art can directly program and implement it on a digital signal processor based on the above disclosure.

[0174] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for coordinated control of fundamental and third harmonic currents of a permanent magnet synchronous motor, characterized in that, The permanent magnet synchronous motor is driven by a three-phase four-bridge inverter, the midpoint of which is connected to the neutral point of the three-phase windings of the motor, providing a flow path for the third harmonic zero-sequence current; the method includes the following in each control cycle: Obtain the stator temperature, rotor electric angular velocity, and load torque of the permanent magnet synchronous motor; The fundamental permanent magnet flux linkage and the third harmonic permanent magnet flux linkage after temperature compensation are calculated based on the stator temperature. The temperature coefficients of the fundamental flux linkage and the third harmonic flux linkage are different and both are negative. The absolute value of the temperature coefficient of the third harmonic flux linkage is greater than the absolute value of the temperature coefficient of the fundamental flux linkage. Calculate the dynamic coupling coefficient, which is the product of the temperature compensation factor, the speed correction factor, and the load correction factor. The temperature compensation factor is the ratio of the third harmonic permanent magnet flux linkage to the fundamental permanent magnet flux linkage at the reference temperature, and the ratio of the third harmonic permanent magnet flux linkage to the fundamental permanent magnet flux linkage after temperature compensation at the current temperature. Calculate the current margin, which is the difference between the maximum current allowed by the controller and the current stator current amplitude. Also calculate the ratio of the current margin to the reference value of the fundamental current amplitude. If the ratio is not greater than the preset threshold, third harmonic injection is prohibited. Otherwise, third harmonic injection is enabled and the smaller of the product of the theoretical optimal harmonic injection coefficient and the dynamic coupling coefficient and the ratio is taken as the optimal harmonic injection coefficient. The ratio of the third harmonic quadrature-axis current setpoint to the fundamental quadrature-axis current setpoint is set to the optimal harmonic injection coefficient. The fundamental quadrature-axis current setpoint and the third harmonic quadrature-axis current setpoint are input to the fundamental current loop controller and the third harmonic current loop controller, respectively. The control quantities of the two current loop controllers are combined after coordinate transformation, and the three-phase four-arm inverter is driven by three-dimensional space vector pulse width modulation.

2. The method for coordinated control of fundamental and third harmonic currents of a permanent magnet synchronous motor according to claim 1, characterized in that: The speed correction coefficient is a piecewise function: when the absolute value of the rotor electric angular velocity is greater than the speed correction threshold, the speed correction coefficient is the ratio of the speed correction threshold to the absolute value of the rotor electric angular velocity; When the absolute value of the rotor's electrical angular velocity is not greater than the speed correction threshold, the speed correction coefficient is equal to 1; the speed correction threshold is taken as 60% to 80% of the motor's rated electrical angular velocity.

3. The method for coordinated control of fundamental and third harmonic currents of a permanent magnet synchronous motor according to claim 1, characterized in that: The load correction factor is 1 plus the load influence factor multiplied by the ratio of the load torque to the rated torque, wherein the load influence factor ranges from 0.05 to 0.

15.

4. The method for coordinated control of fundamental and third harmonic currents of a permanent magnet synchronous motor according to claim 1, characterized in that: The theoretically optimal harmonic injection coefficient is 1 / 6. This value is determined based on the flat-top wave injection principle under peak current constraint: the phase current after injecting the third harmonic exhibits a flat-top wave shape, and the phase current peak value is minimized when the theoretically optimal harmonic injection coefficient is 1 / 6.

5. The method for coordinated control of fundamental and third harmonic currents of a permanent magnet synchronous motor according to claim 1, characterized in that: The electromagnetic torque of the permanent magnet synchronous motor is the sum of the fundamental torque component and the third harmonic torque component. In the third harmonic torque component, the product of the third harmonic permanent magnet flux linkage and the third harmonic cross-axis current is multiplied by a coefficient of 3. The ratio of the third harmonic torque to the fundamental torque is the product of the optimal harmonic injection coefficient, the coefficient of 3, and the ratio of the third harmonic permanent magnet flux linkage to the fundamental permanent magnet flux linkage at the current temperature.

6. The method for coordinated control of fundamental and third harmonic currents of a permanent magnet synchronous motor according to claim 1, characterized in that: Both the fundamental current loop controller and the third harmonic current loop controller adopt a nonlinear active disturbance rejection control structure, each including a tracking differentiator, a second-order nonlinear extended state observer, and a nonlinear state error feedback control law. The second-order nonlinear extended state observer expands the total disturbance into state variables, and calculates the observation error using a piecewise nonlinear function to estimate and compensate for the total disturbance. In the nonlinear state error feedback control law, the nonlinear factor corresponding to the tracking error is greater than 0 and less than 1, and the nonlinear factor corresponding to the differential error is greater than 1.

7. The method for coordinated control of fundamental and third harmonic currents of a permanent magnet synchronous motor according to claim 1, characterized in that: The second-order nonlinear extended state observer uses Euler's method for first-order forward differential discretization, wherein the update term of the total disturbance observation includes the nonlinear function value of the observation error, and the nonlinear function value is negative; the gain of the second-order nonlinear extended state observer is tuned using the bandwidth method, and the observer bandwidth of the third harmonic current loop controller is taken as 1.2 to 2.0 times the observer bandwidth of the fundamental current loop controller.

8. The method for coordinated control of fundamental and third harmonic currents of a permanent magnet synchronous motor according to claim 1, characterized in that: The load torque is extracted from the expansion state of the third-order nonlinear expansion state observer of the velocity outer loop after deducting the damping term and the mechanical angular velocity conversion term; or it is calculated according to the equation of motion based on the differential of electromagnetic torque, moment of inertia, rotor mechanical angular velocity and damping coefficient.

9. The method for coordinated control of fundamental and third harmonic currents of a permanent magnet synchronous motor according to claim 1, characterized in that: The three-dimensional spatial vector pulse width modulation is implemented in the abc coordinate system. The 16 switching states of the three-phase four-arm inverter correspond to 14 non-zero switching voltage vectors and 2 zero switching voltage vectors, which form a dodecahedron in three-dimensional space and are divided into 24 spatial tetrahedrons. The spatial tetrahedron where the reference voltage vector is located is located by the pointer function and the duty cycle is solved. The fundamental direct-axis current setpoint and the third harmonic direct-axis current setpoint are both set to zero.

10. A co-current control system for the fundamental and third harmonic currents of a permanent magnet synchronous motor, characterized in that, The system includes a three-phase four-arm inverter, a surface-mount permanent magnet synchronous motor, a temperature sensor, a current sensor, a position sensor, and a digital signal processor. The midpoints of the first three arms of the three-phase four-arm inverter are respectively connected to the three-phase windings of the surface-mount permanent magnet synchronous motor, and the midpoint of the fourth arm is connected to the neutral point of the three-phase windings of the surface-mount permanent magnet synchronous motor. A filter inductor is connected in series on the neutral line between the midpoint of the fourth arm and the neutral point. The digital signal processor stores a computer program, which, when executed, implements the method according to any one of claims 1 to 9.

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