Phase-locked loop control method of permanent magnet synchronous generator

Abstract

The invention discloses a phase-locked loop control method of a permanent magnet synchronous generator, which belongs to the technical field of motor control and wind power generation, and comprises the following steps: acquiring two-phase current and two-phase voltage under a static coordinate system, and calculating through a sliding-mode observer to obtain a shaft and an extended counter electromotive force estimated value of the shaft; designing a finite position set phase-locked loop based on Taylor series and a Newton iteration method, performing quadrant judgment and correction processing on a rotor position estimation value after primary iteration to obtain a final rotor position estimation value, performing differential operation on the final rotor position estimation value, and processing a differential result by using a low-pass filter to obtain a final rotor position estimation value; obtaining a rotating speed estimation value of a rotor, and integrating the sliding-mode observer and a finite position set phase-locked loop to a motor vector control system to realize position sensorless control; according to the phase-locked loop control method of the permanent magnet synchronous generator, the calculation burden is greatly reduced while the precision is ensured.

Description

Technical Field

[0001] This invention relates to the fields of motor control and wind power generation technology, and in particular to a phase-locked loop control method for a permanent magnet synchronous generator. Background Technology

[0002] Permanent magnet synchronous generators (PMSGs), with their high reliability, high efficiency, and high power density, have become one of the core technologies in modern large-scale wind turbine generators, especially in the offshore wind power field where technical barriers are high and reliability requirements are stringent. Achieving high-performance vector control requires precise rotor position and speed information. Traditional methods rely on mechanical position sensors (such as encoders and resolvers), but these sensors operate in harsh environments in wind power plants for extended periods, are susceptible to electromagnetic interference, and suffer from reduced reliability, increased costs, and maintenance difficulties.

[0003] Sensorless control technology is key to solving the above problems. The PMSG sensorless control strategy based on the fundamental wave model utilizes information such as back electromotive force or flux linkage to extract rotor information, making it suitable for medium- and high-speed operating ranges and an ideal choice for the main operating range of wind turbine generators. Estimation methods based on sliding mode observers (SMOs) have been widely used in sensorless control due to their advantages such as simple structure, strong robustness, and fast dynamic response. Extracting rotor position information from the observed flux linkage signal typically relies on a phase-locked loop (PLL); however, traditional PI-type PLLs (PI-PLLs) suffer from drawbacks such as complex parameter tuning, slow dynamic response, limited bandwidth, and poor robustness.

[0004] In recent years, the concept of Finite Control Set Model Predictive Control (FCS-MPC) has been introduced into position estimation, forming the Finite Position Set Phase-Locked Loop (FPS-PLL). FPS-PLL estimates position by constructing a cost function and searching for its minimum, requiring no parameter tuning and exhibiting fast dynamic response. However, existing FPS-PLL methods typically require multiple iterations to achieve high accuracy, resulting in a heavy computational burden and high demands on the computational power of the digital controller. This makes them unsuitable for implementation in systems with high switching frequencies and also increases system cost.

[0005] Therefore, there is an urgent need in this field for a sensorless phase-locked loop control method that can significantly reduce computational complexity while ensuring high-precision position estimation, and is particularly suitable for wind power generation applications with extremely high requirements for reliability and dynamic performance. Summary of the Invention

[0006] The purpose of this invention is to provide a phase-locked loop control method for permanent magnet synchronous generators, in order to solve the problems of complex parameter tuning and insufficient dynamic performance of traditional PI-type phase-locked loops (PI-PLLs) in the prior art, as well as the problems of numerous iterations and heavy computational burden of traditional finite position set phase-locked loops (FPS-PLLs).

[0007] To achieve the above objectives, the present invention provides a phase-locked loop control method for a permanent magnet synchronous generator, comprising the following steps: S1. Obtain the three-phase current and three-phase voltage of the permanent magnet synchronous generator, and after Clarke transformation, obtain the values ​​in stationary coordinates. The two-phase current and two-phase voltage under the system; S2, calculated using a sliding mode observer based on two-phase current and two-phase voltage. shaft and The extended back electromotive force estimate of the shaft; S3. Design a finite position set phase-locked loop based on Taylor series and Newton's iteration method. This includes using the extended back EMF estimate to quickly calculate the initial estimate of the rotor position using the approximate formula of Taylor series expansion. Starting from the initial estimate, Newton's iteration method is used to perform one iteration calculation, and the rotor position estimate after one iteration is output. S4. Perform quadrant judgment and correction on the rotor position estimate after one iteration to obtain the final rotor position estimate. S5. Perform a differential operation on the final rotor position estimate, process the differential result with a low-pass filter, and obtain the rotor speed estimate. S6. Integrate the sliding mode observer and the finite position phase-locked loop into the motor vector control system to achieve sensorless control.

[0008] Preferably, the mathematical model of the sliding mode observer in S2 includes: A permanent magnet synchronous generator based on extended back electromotive force at rest Voltage equation in coordinate system: ; in, , , , They are respectively shaft and The motor voltage and current of the shaft. For stator resistance, The electric angular velocity of the motor. and They are respectively shaft and The inductance of the shaft, and They are respectively shaft and The extended back electromotive force of the shaft is specifically expressed as: ; in, For rotor position, To extend the amplitude of the back electromotive force, it is specifically expressed as follows: ; in, It is a permanent magnet flux chain. For differential operators, and They are respectively shaft and The current in the shaft; Based on this, the state equation of the permanent magnet synchronous generator is: ; The constructed sliding mode observer is as follows: ; in, and They are respectively shaft and The observed current of the axis, and They are respectively shaft and The sliding mode control function for the axis is specifically expressed as follows: ; in, It is a saturation function. This is the sliding mode gain.

[0009] Preferably, the extended back EMF estimate in S2 is obtained by passing the sliding mode control function through a low-pass filter, the transfer function of which in the complex frequency domain is: ; in, and They are respectively shaft and The extended back electromotive force estimate of the shaft, This is the cutoff frequency of the low-pass filter. For the Laplace operator.

[0010] Preferably, the specific steps in S3 for quickly calculating the initial estimate of the rotor position using the approximate formula of Taylor series expansion are as follows: a. Based on the estimated extended back electromotive force. and Calculate their ratio As input variables; b. Determine the relationship between the absolute value of the input variable and 1. If it is greater than 1, take the reciprocal to ensure that the input variable is between [-1, 1]. c. When the absolute value of the input variable is in the range (0.5, 1], compress its range to the range [-1 / 2, 1 / 2] through variable transformation, and then use the first two terms of the Taylor expansion for calculation; d. Based on the processed input variables, the initial estimate of the rotor position is calculated using the corresponding Taylor series approximation formula.

[0011] Preferably, the formula for calculating the initial estimate of the rotor position is: ; in, This is the initial estimate of the rotor position.

[0012] Preferably, the specific steps for performing one iteration calculation using Newton's iteration method in S3 are as follows: a. Constructing the cost function The specific formula is as follows: ; in, This represents the error between the actual and estimated rotor position. b. Calculate the first and second derivatives of the cost function; ; ; c. Perform one Newton iteration operation to obtain the rotor position estimate after one iteration; ; in, This is the rotor position estimate after one iteration.

[0013] Preferably, the formula for quadrant determination and correction in S4 is: ; in, This is the final estimated rotor position value.

[0014] Therefore, the phase-locked loop control method for a permanent magnet synchronous generator described above has the following beneficial effects: (1) This invention combines fast initial value calculation based on Taylor series with one Newton iteration. Since the initial value itself has extremely high precision, and by utilizing the superlinear convergence characteristic of Newton's method, only one iteration is needed to limit the theoretical error of rotor position estimation to an extremely low level. Compared with the existing FPS-PLL method that requires multiple iterations, the computational load is significantly reduced, making the algorithm easy to implement on low-cost DSPs and suitable for systems with high switching frequencies.

[0015] (2) This invention avoids the dynamic lag problem caused by the controller bandwidth limitation of traditional PI-PLL; when the motor speed or load changes suddenly, it can track the real rotor position more quickly and exhibit better dynamic performance.

[0016] (3) The core of this invention is a deterministic mathematical operation process that does not include any controller parameters (such as PI parameters) that require complex tuning. This greatly simplifies engineering applications and improves the consistency and reliability of the system.

[0017] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] Figure 1 This is a flowchart of a phase-locked loop control method for a permanent magnet synchronous generator according to the present invention; Figure 2 This is a flowchart of a finite position set phase-locked loop algorithm for a phase-locked loop control method for a permanent magnet synchronous generator according to the present invention. Detailed Implementation

[0019] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0020] Example like Figure 1 As shown, this invention provides a phase-locked loop control method for a permanent magnet synchronous generator. This method is implemented within the framework of a motor vector control system and specifically includes the following steps: S1. Set the motor parameters, sliding mode observer parameters, and finite position phase-locked loop parameters of the permanent magnet synchronous generator. Acquire the three-phase current and three-phase voltage of the permanent magnet synchronous generator in each control cycle. Perform Clarke transformation to obtain the values ​​in stationary coordinates. The two-phase current is controlled by the inverter. The two-phase voltage output by the inverter is obtained through voltage sensors or voltage commands from the SVPWM module.

[0021] S2, calculated using a sliding mode observer based on two-phase current and two-phase voltage. shaft and The extended back electromotive force estimate of the shaft.

[0022] The mathematical model of the sliding mode observer includes: A permanent magnet synchronous generator based on extended back electromotive force at rest Voltage equation in coordinate system: ; in, , , , They are respectively shaft and The motor voltage and current of the shaft. For stator resistance, The electric angular velocity of the motor. and They are respectively shaft and The inductance of the shaft, and They are respectively shaft and The extended back electromotive force of the shaft is specifically expressed as: ; in, For rotor position, To extend the amplitude of the back electromotive force, it is specifically expressed as follows: ; in, It is a permanent magnet flux chain. For differential operators, and They are respectively shaft and The current in the shaft; Based on this, the state equation of the permanent magnet synchronous generator is: ; The constructed sliding mode observer is as follows: ; in, and They are respectively shaft and The observed current of the axis, and They are respectively shaft and The sliding mode control function for the axis is specifically expressed as follows: ; in, It is a saturation function. This is the sliding mode gain.

[0023] The extended back EMF estimate is obtained by passing the sliding mode control function through a low-pass filter, the transfer function of which in the complex frequency domain is: ; in, and They are respectively shaft and The extended back electromotive force estimate of the shaft, This is the cutoff frequency of the low-pass filter. For the Laplace operator.

[0024] S3. Design a finite-position set phase-locked loop based on Taylor series and Newton's iteration method. The algorithm flow of the finite-position set phase-locked loop is as follows: Figure 2 As shown, the method includes using an approximate formula based on the extended back electromotive force estimate to quickly calculate the initial estimate of the rotor position using the Taylor series expansion. Starting from the initial estimate, the method uses Newton's iteration method to perform one iteration calculation and outputs the rotor position estimate after one iteration.

[0025] The specific steps for quickly calculating the initial estimate of the rotor position using the approximate formula of Taylor series expansion are as follows: a. Based on the estimated extended back electromotive force. and Calculate their ratio As input variables; b. Determine the relationship between the absolute value of the input variable and 1. If it is greater than 1, take the reciprocal to ensure that the input variable is between [-1, 1]. c. When the absolute value of the input variable is in the interval (0.5, 1], perform variable transformation. After compressing its range to the interval [-1 / 2, 1 / 2], the first two terms of the Taylor expansion are used for calculation to obtain higher initial accuracy; d. Based on the processed input variables, the initial estimate of the rotor position is calculated using the corresponding Taylor series approximation formula.

[0026] The formula for calculating the initial estimate of the rotor position is: ; in, This is the initial estimate of the rotor position.

[0027] Using the initial estimate of the rotor position as the initial value, Newton's iteration method is applied for one iteration. The specific steps for performing one iteration calculation using Newton's iteration method are as follows: a. Constructing the cost function The specific formula is as follows: ; in, This represents the error between the actual and estimated rotor position. b. Calculate the first and second derivatives of the cost function; ; ; c. Perform one Newton iteration operation to obtain the rotor position estimate after one iteration; ; in, This is the rotor position estimate after one iteration.

[0028] S4. Perform quadrant judgment and correction on the rotor position estimate after one iteration to obtain the final rotor position estimate.

[0029] The formula for quadrant determination and correction is: ; in, This is the final estimated rotor position value.

[0030] Because of the high accuracy of the initial values, the theoretical error in estimating the rotor position can be limited to 4.96 × 10⁻⁶ after only one iteration. -8 Within rad, it achieves extremely high accuracy.

[0031] S5. Perform a differential operation on the final rotor position estimate, process the differential result with a low-pass filter, and obtain the rotor speed estimate. S6. Integrate the sliding mode observer and the finite position phase-locked loop into the motor vector control system, and feed back the estimated rotor position and speed values ​​to the coordinate transformation and speed loop of the motor vector control system to achieve sensorless control and complete the closed-loop control of the entire motor vector control system.

[0032] To verify the effectiveness and superiority of the method proposed in this embodiment, a system simulation experiment was conducted. The dynamic performance of the method in this embodiment and the traditional PI-PLL method was tested when the motor speed underwent a step change. The key performance indicators are compared in the table below: Table 1. Experimental results of rotational speed variation

[0033] As shown in Table 1, compared with the traditional PI-PLL, the method proposed in this embodiment reduces the maximum error of rotor position estimation by approximately 22.7%, indicating higher estimation accuracy. It also shortens the system's dynamic response time by approximately 37%, demonstrating faster tracking speed during sudden speed changes. During the dynamic process, the motor's phase current fluctuations are significantly smaller (peak value reduced by 31.3%), indicating that the method of this invention provides smoother torque control, contributing to improved overall system stability and reliability.

[0034] To further illustrate the high-precision characteristics of the method in this embodiment, numerical simulations were performed for the "one Newton iteration" step. As shown in Table 2, even under different initial errors, the estimation error can be rapidly compressed to an extremely low level after only one Newton iteration.

[0035] Table 2 Iteration Results Since the initial value based on the Taylor series expansion already possesses high accuracy, using this as a starting point and performing only one Newton iteration can reduce the position estimation error from 10... -3 The magnitude rapidly decreased to 10 -8 Up to 10 -10 This demonstrates that the method described in this embodiment can achieve theoretical accuracy far exceeding actual engineering requirements with extremely low computational overhead (only one iteration), perfectly balancing the contradiction between computational efficiency and estimation accuracy.

[0036] Therefore, this invention employs the aforementioned phase-locked loop control method for a permanent magnet synchronous generator. By combining Taylor expansion initial value selection with Newton's iteration method, high-precision rotor position estimation can be achieved in just one iteration. This significantly reduces the computational burden while maintaining accuracy, making it suitable for digital control systems and eliminating the need for parameter tuning. It is particularly suitable for applications with limited computing resources and complex operating conditions, such as wind power generation.

[0037] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A phase-locked loop control method of a permanent magnet synchronous generator, characterized by, The method comprises the following steps: S1, acquiring three-phase current and three-phase voltage of the permanent magnet synchronous generator, through Clarke transformation, obtaining two-phase current and two-phase voltage in static coordinate system S2, based on the two-phase currents and the two-phase voltages, is calculated by a sliding mode observer axes and axes and S3, design a limited position set phase-locked loop based on Taylor series and Newton iteration method, including based on the extended back electromotive force estimation value, using the approximate formula of Taylor series expansion to quickly calculate the initial estimation value of the rotor position, taking the initial estimation value as the starting point, using Newton iteration method to perform one iteration calculation, and outputting the rotor position estimation value after one iteration; S4, quadrant judgment and correction processing are performed on the rotor position estimation value after one iteration to obtain the final rotor position estimation value; S5, differential operation is performed on the final rotor position estimation value, and the differential result is processed by a low-pass filter to obtain the rotor speed estimation value; S6, the sliding mode observer and the limited position set phase-locked loop are integrated into the motor vector control system to realize the position sensorless control.

2. The phase-locked loop control method of a permanent magnet synchronous generator according to claim 1, characterized by, The mathematical model of the sliding mode observer in S2 comprises: Permanent magnet synchronous generator based on extended back electromotive force in stationary Voltage equation in stationary coordinate system: ； wherein , , , are the motor voltages, currents, are the motor voltages, currents, are the motor voltages, currents, is the stator resistance, is the motor electrical angular velocity, and are the motor inductances, and are the motor inductances, and are the motor inductances, and are the motor extended back electromotive forces, expressed as: ； wherein, is the rotor position, is the extended back EMF amplitude, which is specifically expressed as: ； wherein is the permanent magnet flux linkage, is the differential operator, and are respectively the current of the axis and the current of the axis Based on this, the state equation of the permanent magnet synchronous generator is: ； The constructed sliding mode observer is: ； wherein and are respectively the observed current of the axis, and and are respectively the sliding mode control function of the axis, and are respectively ； wherein is a saturation function, is a sliding mode gain.

3. The phase-locked loop control method of a permanent magnet synchronous generator according to claim 2, characterized by, The extended back electromotive force estimation value in S2 is obtained by passing the sliding mode control function through a low-pass filter, and the transfer function of the low-pass filter in the complex frequency domain is: ； wherein and are respectively axes and an extended back-EMF estimate of the axis, is a low-pass filter cut-off frequency, is a Laplacian operator.

4. The phase-locked loop control method of a permanent magnet synchronous generator according to claim 3, characterized by, The specific steps of using the approximate formula of Taylor series expansion to quickly calculate the initial estimation value of the rotor position in S3 are: a. the estimated extended back emf estimate and , the ratio of which is calculated as an input variable; b. judge the size relationship between the absolute value of the input variable and 1, if greater than 1, take the reciprocal to calculate, ensure that the input variable is in [-1, 1]; c. when the absolute value of the input variable is in the interval (0.5, 1], the range is compressed to [-1 / 2, 1 / 2] through variable transformation, and the first two terms of Taylor expansion formula are used for calculation; d. based on the processed input variable, the corresponding Taylor series approximate formula is used to calculate the initial estimation value of the rotor position.

5. The phase-locked loop control method of a permanent magnet synchronous generator according to claim 4, characterized by, The calculation formula of the initial estimation value of the rotor position is: ； wherein, is an initial estimate of the rotor position.

6. The phase-locked loop control method of a permanent magnet synchronous generator according to claim 2, characterized by, The specific steps of using Newton iteration method to perform one iteration calculation in S3 are: a. Constructing the cost function The specific formula is as follows: ； wherein is the error between the true and estimated rotor position values; b. calculate the first and second derivatives of the cost function; ； ； c. perform one Newton iteration operation to obtain the rotor position estimation value after one iteration; ； wherein, is the rotor position estimate after one iteration.

7. The phase-locked loop control method of a permanent magnet synchronous generator according to claim 6, characterized by, The formula for performing quadrant judgment and correction processing in S4 is: ； wherein, is the final resulting rotor position estimate.

Images