SOGI-QNPLL-based permanent magnet synchronous motor non-inductive vector control method

Abstract

The invention discloses a permanent magnet synchronous motor non-inductive vector control method based on SOGI-QNPLL. The method comprises the following steps: constructing a current state equation of a permanent magnet synchronous motor under a two-phase static coordinate system; constructing a new switching function, and designing and improving a full-order sliding mode observer according to the new switching function and the current state equation; the convergence of the improved full-order sliding mode observer is analyzed, and the value ranges of the gain m and the gain n of the improved full-order sliding mode observer are calculated; analyzing the improved full-order sliding-mode observer, and discretizing the improved full-order sliding-mode observer by adopting a forward Euler method; establishing a phase-locked loop (PLL), performing normalization design on the phase-locked loop, and establishing a normalized phase-locked loop (QNPLL); a second-order generalized integrator (SOGI) is established and discretized by adopting a bilinear transformation method, the discrete SOGI is combined with the QNPLL to form SOGI-QNPLL, and the SOGI-QNPLL is utilized to estimate the rotor position. According to the SOGI-QNPLL provided by the invention, the rotor position can be accurately extracted, the observation precision is remarkably improved, and the reliability and performance of the system are enhanced.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet synchronous motor system control, and particularly to a sensorless vector control method for permanent magnet synchronous motors based on SOGI-QNPLL. Background Technique

[0002] The high-precision control of permanent magnet synchronous motors traditionally relies on mechanical position or speed sensors to provide real-time rotor information. However, this traditional method has many limitations: the physical installation of sensors not only increases the system's moment of inertia and axial dimensions, but also significantly raises the manufacturing cost. At the same time, the introduction of mechanical components may reduce the overall reliability of the system. Especially under harsh working conditions such as extreme temperatures, high-speed rotation, or strong electromagnetic interference, the application feasibility of sensors is severely restricted. Based on this background, sensorless control technology has emerged. It achieves accurate estimation of rotor information through advanced signal processing and state observation algorithms and has now become a forefront research hotspot in the field of modern motor drives.

[0003] The traditional sliding mode observer (SMO) is a non-linear observation method based on variable structure control, which is widely used in the sensorless control system of permanent magnet synchronous motors to estimate the rotor position and speed. Its core idea is to construct a sliding mode surface so that the system state converges to the desired trajectory within a finite time, thereby achieving accurate observation of the back electromotive force (Back-EMF), and then solving the rotor position information.

[0004] In the motor angle estimation based on the traditional sliding mode observer, there are several key technical challenges in the system. Since the observer uses discontinuous switching control strategies such as the sign function, it will inevitably cause significant high-frequency chattering phenomena. This chattering appears as high-frequency noise interference in the time domain and a wide-band spectrum distribution in the frequency domain. It will not only seriously contaminate the observed signal of the back electromotive force, but also lead to a significant deterioration in the estimation accuracy of the rotor position and speed. At the same time, in the traditional method, only the back electromotive force signal before filtering is used as feedback when calculating the estimated current. However, this signal contains a large amount of high-frequency noise, resulting in inaccurate observed values.

[0005] To suppress this phenomenon, low-pass filters are usually introduced for signal conditioning in engineering practice. However, this processing method brings new technical problems: on the one hand, the phase lag characteristic of the filter will reduce the dynamic response performance of the system; on the other hand, the non-ideality of the amplitude-frequency characteristic will cause a steady-state error in angle calculation, thus forming an inherent contradiction between control accuracy and system response speed. Summary of the Invention

[0006] The object of the present invention is to solve the problems mentioned in the existing background art, and to provide a sensorless vector control method for a permanent magnet synchronous motor based on SOGI-QNPLL.

[0007] A sensorless vector control method for a permanent magnet synchronous motor based on SOGI-QNPLL includes the following steps:

[0008] Step 1, constructing the current state equation of the permanent magnet synchronous motor in the two-phase stationary coordinate system;

[0009] Step 2, constructing a new switching function, and designing an improved full-order sliding mode observer according to the new switching function and the current state equation;

[0010] Step 3, analyzing the convergence of the improved full-order sliding mode observer, and calculating the value ranges of the gains m and n of the full-order sliding mode observer;

[0011] Step 4, analyzing the improved full-order sliding mode observer, and discretizing the improved full-order sliding mode observer by using the forward Euler method;

[0012] Step 5, building a phase-locked loop (PLL), performing a normalization design on the phase-locked loop, and building a normalized phase-locked loop (QNPLL);

[0013] Step 6, building a second-order generalized integrator (SOGI) and discretizing it by using the bilinear transformation method, combining the discrete SOGI with the QNPLL to form a SOGI-QNPLL, and using it to estimate the rotor position.

[0014] The current state equation of the permanent magnet synchronous motor in the two-phase stationary coordinate system in the said Step 1 is wherein, u α , u β are the voltages on the α-axis and β-axis respectively, i α , i β are the currents on the α-axis and β-axis respectively, L d , L q are the d-axis and q-axis inductances respectively, R s is the stator resistance, ω e is the electrical angular velocity, E α , E β is the extended back electromotive force;

[0015] The extended back electromotive force in the said Step 1 is wherein, θ e is the electrical angular position of the rotor, ψ f is the permanent magnet flux linkage.

[0016] The new switching function in the said Step 2 is In the formula, sign(s) is the sign function, σ represents the boundary layer thickness of the function fanp(s), and 0 < σ < 1, β > 1;

[0017] The improved full-order sliding mode observer in step 2 is In the formula, is the observed value of the stator current, is the observed value of the extended back electromotive force, B = -L d ·I, D = 1 / L d ·I, is the observed electrical angular velocity, u s = [u α u β T , K is the feedback gain matrix, m and n are the gains of the improved full-order sliding mode observer, fanp(s) is the new switching function proposed by the present invention.

[0018] In step 3, in order to ensure the asymptotic stability of the improved full-order sliding mode observer, the condition that the gain m of the improved full-order sliding mode observer must satisfy is In the formula, is the current observation error and satisfies is the observed error of the extended back electromotive force and satisfies

[0019] In step 3, in order to ensure the asymptotic stability of the improved full-order sliding mode observer, the condition that the gain n of the improved full-order sliding mode observer must satisfy is In the formula, L is the inductance of the permanent magnet synchronous motor and satisfies L = L d = L q , is the observed error of the electrical angular velocity and satisfies

[0020] The observed back electromotive force in step 4 can be expressed as In the formula, This term represents It has the characteristics of a second-order low-pass filter, which can filter out the high-frequency noise of the system, so there is no need to use a low-pass filter for filtering, thus avoiding the phase lag and back electromotive force amplitude attenuation problems caused by the use of a low-pass filter;

[0021] The discretized formula of the improved full-order sliding mode observer in step 4 is In the formula, T s is the sampling time, is the value of the observed current at the current moment,​ Observe the value of the current at the next moment, is the value of the back electromotive force at the current moment for observation, Observe the value of the back electromotive force at the next moment,

[0022] The transfer function of the PLL in step 5 described above is In the formula, is the electrical angle of the observed rotor position, K smop and K smoi are the parameters of the PI regulator;

[0023] The transfer function of the QNPLL in step 5 described above is In the formula, ω n is the undamped natural oscillation frequency and satisfies The proportional coefficient is K smop = 2ξω n , ξ is the damping ratio, and the integral coefficient is

[0024] The closed-loop transfer function of the SOGI in step 6 described above is In the formula, v is the input signal, v' and qv' are the output signals, where v' has the same phase and amplitude as the fundamental wave of v while qv' lags by 90°, k affects the bandwidth of the closed-loop system, and ω is the resonance frequency of the SOGI;

[0025] The expression of the discretized SOGI in step 6 described above is In the formula, T s is the sampling time.

[0026] Advantages of the present invention:

[0027] 1. The present invention proposes a new switching function fanp(s, σ). Compared with the traditional sign(s) function, this new function can significantly reduce the chattering amplitude of the system; compared with the sat(s, σ) function and the tanh(s, σ) function, the new function fanp(s, σ) can effectively shorten the convergence time, thus showing superior performance in reducing chattering and accelerating convergence.

[0028] 2. The present invention proposes an improved full-order sliding mode observer, which incorporates the characteristics of a second-order low-pass filter and can effectively filter out high-frequency noise in the back electromotive force without the need for an additional low-pass filter. The improved full-order sliding mode observer can feedback the estimated value of the back electromotive force to the current observation link, and through this feedback mechanism, the observation accuracy is improved, thereby optimizing the overall performance of the system.

[0029] 3. The SOGI-QNPLL proposed by the present invention can accurately extract the rotor position, significantly improving the observation accuracy and enhancing the reliability and performance of the system. At the same time, the system performance is no longer affected by the speed change, making the design of the orthogonal phase-locked loop parameters more convenient. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is a flowchart of an embodiment of the present invention;

[0031] Figure 2 is a system block diagram of sensorless vector control of a permanent magnet synchronous motor according to an embodiment of the present invention;

[0032] Figure 3 is a phase diagram of a switching function according to an embodiment of the present invention;

[0033] Figure 4 is a block diagram of a PLL phase-locked loop structure according to an embodiment of the present invention;

[0034] Figure 5 is an equivalent block diagram of a PLL phase-locked loop according to an embodiment of the present invention;

[0035] Figure 6 For an embodiment of the present invention with ω e is the root locus diagram of a phase-locked loop system with variable parameters;

[0036] Figure 7 is a block diagram of a SOGI structure according to an embodiment of the present invention;

[0037] Figure 8 is a discretized SOGI structure block diagram according to an embodiment of the present invention;

[0038] Figure 9 is a block diagram of a SOGI-QNPLL structure according to an embodiment of the present invention;

[0039] Figure 10 is a Lissajous figure diagram of the observed back electromotive force and the observed back electromotive force according to an embodiment of the present invention;

[0040] Figure 11 is a comparison diagram of the observed rotor position according to an embodiment of the present invention;

[0041] Figure 12 is a comparison diagram of the observed rotor position error according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0042] Please refer to Figures 1 to 12 as shown, which is an embodiment of the present invention.

[0043] Combined with Figure 1, which is a sensorless vector control method for permanent magnet synchronous motors based on SOGI-QNPLL. The system block diagram of the sensorless vector control of the permanent magnet synchronous motor provided in this embodiment is shown in Figure 2 , where SOGI-QNPLL and the improved full-order sliding mode observer are the contents disclosed in this embodiment.

[0044] Specifically, it includes the following steps:

[0045] Step 1, construct the current state equation of the permanent magnet synchronous motor in the two-phase stationary coordinate system;

[0046] The current state equation of the permanent magnet synchronous motor in the two-phase stationary coordinate system is

[0047]

[0048] In the formula, u α , u β are the α-axis and β-axis voltages respectively, i α , i β are the α-axis and β-axis currents respectively, L d , L q are the d-axis and q-axis inductances respectively, R s is the stator resistance, ω e is the electrical angular velocity, E α , E β is the extended back electromotive force and satisfies the following expression

[0049]

[0050] In the formula, θ e is the electrical angular position of the rotor, ψ f is the permanent magnet flux linkage.

[0051] Rewrite the voltage equation (1) into the form of the current state equation:

[0052]

[0053] Step 2, construct a new switching function, and design an improved full-order sliding mode observer according to the new switching function and the current state equation;

[0054] Combined with Figure 3 shown, the new switching function proposed in this embodiment is

[0055]

[0056] In the formula, sign(s) is the sign function, σ represents the boundary layer thickness of the function fanp(s), and 0 < σ < 1, β > 1;

[0057] Since the change rate of the stator current within one sampling period is much greater than that of the electrical angular velocity, assume Since it is a surface-mounted motor, L = L q = L d And θ e = ω e t. Differentiating the extended back electromotive force in Equation (2) gives

[0058]

[0059] Based on Equation (3), adding the state variable equation of Equation (5) gives

[0060]

[0061] Where, i s = [i α i β T , E s = [E α E β T , u s = [u α u β T , A = -R s / L d ·I + ω e (L d -L q ) / L d ·J, B = -L d ·I, C = ω e ·J, D = 1 / L d ·I, where

[0062] Design a high-order sliding mode observer as follows

[0063]

[0064] Where is the observed value of the stator current, is the observed value of the extended back electromotive force, is the observed electrical angular velocity, K is the feedback gain matrix, m and n are the gains of the improved full-order sliding mode observer, fanp(s) is the new switching function proposed by the present invention.

[0065] Step 3, analyze the convergence of the improved full-order sliding mode observer, and calculate the value ranges of the gains m and n of the improved full-order sliding mode observer;

[0066] For a surface-mounted motor, it can be obtained that L = L​​​q = L d Subtracting Equation (6) from Equation (7), the error dynamic equation of current estimation is obtained as

[0067]

[0068] where is the current observation error, is the observation error of the extended back electromotive force;

[0069] To analyze the convergence of the improved full-order sliding mode observer, the Lyapunov function is selected as

[0070]

[0071] Differentiating Equation (9) gives

[0072]

[0073] To ensure the stability of the full-order sliding mode observer, i.e., the gain m of the full-order sliding mode observer must satisfy the following conditions

[0074]

[0075] When V1 decays to zero, and will be controlled to zero, that is, the estimated current will converge to the actual value. According to Equation (8), if the estimated speed is accurate enough, when the sliding mode motion occurs, the equivalent control of the two discontinuous high-switch control elements can be extracted as follows

[0076]

[0077] Subtracting Equation (6) from Equation (7), the error dynamic equation of the extended electromotive force is

[0078]

[0079] where is the observation error of the electrical angular velocity.

[0080] Substituting Equation (12) into Equation (13) gives

[0081]

[0082] where

[0083] Define the Lyapunov function of the back electromotive force as

[0084]

[0085] Derive the derivative of Equation (15) to obtain

[0086]

[0087] To ensure the stability of the back electromotive force observer and the existence of the sliding mode surface, it is necessary to satisfy Obtain

[0088]

[0089] Step 4: Analyze the improved full-order sliding mode observer and discretize the improved full-order sliding mode observer using the forward Euler method;

[0090] According to Equations (7) and (12), we can obtain

[0091]

[0092] The back electromotive force can be expressed in the following form from the above Equation (18)

[0093]

[0094] where This term represents It has the characteristics of a second-order low-pass filter, which can filter out the high-frequency noise of the system. Therefore, there is no need to use a low-pass filter for filtering, thus avoiding the phase lag and back electromotive force amplitude attenuation problems caused by the use of a low-pass filter.

[0095] In the actual application of motor control, digital control methods are generally adopted. To make the simulation model more consistent with the actual use effect, Equation (7) is discretized using the forward Euler method as follows

[0096]

[0097] where T s is the sampling time, is the value of the observed current at the current moment, the value of the observed current at the next moment, is the value of the observed back electromotive force at the current moment, the value of the observed back electromotive force at the next moment.

[0098] Simplify Equation (20) to obtain

[0099]

[0100] Step 5: Build a phase-locked loop (PLL), perform normalized design on the phase-locked loop, and build a normalized phase-locked loop (QNPLL);

[0101] Since the sliding mode control is accompanied by high-frequency chattering in the sliding mode, which results in a large angle estimation error, a phase-locked loop (PLL) structure is introduced to extract the rotor position, as Figure 4 shown.

[0102] When , To observe the electrical angle of the rotor position, from Equation (2) and Figure 4 it can be obtained that

[0103]

[0104] wherein

[0105] The equivalent block diagram of the PLL is as Figure 5 shown, and thus the transfer function from to θ e is

[0106]

[0107] For a surface-mounted motor, it can be obtained that L = L q = L d , so k = ω e ψ f , and K smop and K smoi are the parameters of the PI regulator.

[0108] Substituting into Equation (23) and arranging, the characteristic equation is as follows

[0109]

[0110] After determining the PI regulator parameters K smop and K smoi , the root locus of the PLL position tracker with the rotational speed ω e as the variable parameter can be obtained, as Figure 6 shown. It can be seen that when K smop and K smoi are constants, the system poles will move in the s-plane with the change of the rotational speed ω e , which will affect the dynamic performance of the PLL position observer and bring inconvenience to the parameter design.

[0111] From the analysis of the closed-loop system bandwidth, assuming the system bandwidth frequency is ω b , substituting s = jω b into Equation (24) gives

[0112]

[0113] where: k = ω e ψ f .

[0114] It can be seen that the bandwidth of the system changes with the rotational speed ω e To eliminate the above influence, in this section, an extended back electromotive force normalization link is introduced into the phase-locked loop structure to obtain the normalized phase-locked loop (NQPLL). After considering the back electromotive force normalization link, the closed-loop transfer function of the system is Equation (26), and the system performance no longer changes with the rotational speed ω e and thus it is convenient for the design of the orthogonal phase-locked loop parameters.

[0115]

[0116] From the transfer function of the second-order system, it can be obtained that

[0117]

[0118] where ω n is the undamped natural oscillation frequency and satisfies The proportionality coefficient is K smop = 2ξω n , ξ is the damping ratio, and the integral coefficient is

[0119] Step 6: Build a second-order generalized integrator (SOGI) and discretize it using the bilinear transformation method. Combine the discrete SOGI with the QNPLL to form the SOGI-QNPLL, and use it to estimate the rotor position.

[0120] The second-order generalized integrator (SOGI) is an advanced signal processing tool that can comprehensively consider the integral and rate of change of the input signal. Compared with the first-order integrator, it has more flexible response characteristics, stronger interference suppression ability, and higher control accuracy, and is widely used in power electronic systems to improve system performance and stability. The structure diagram is shown in Figure 7, where v is the input signal, v' and qv' are the output signals, and v' has the same phase and amplitude as the fundamental wave of v while qv' lags by 90°.

[0121] The closed-loop transfer function of the SOGI is

[0122]

[0123] where k affects the bandwidth of the closed-loop system, and ω is the resonance frequency of the SOGI.

[0124] To be able to use it in a discrete system, it is discretized. The present invention uses the bilinear transformation, and the expression is as follows

[0125]

[0126] where T s is the sampling time.

[0127] In this method, is approximated as Substituting into Equation (29) and simplifying gives

[0128]

[0129] To further simplify, the following assumptions are made

[0130]

[0131] Then Equation (30) is rewritten as

[0132]

[0133] Substitute and into Equation (32), and the discretized key expression of SOGI can be obtained as

[0134]

[0135] The discretized SOGI block diagram is as shown in Figure 8 where w = 2T s ω. Combining the discretized SOGI and QNPLL gives SOGI-QNPLL, as shown in Figure 9 shown.

[0136] To verify the effectiveness of this control method, a simulation model of this control method was constructed in the MATLAB / Simulink environment to verify the performance of the control method.

[0137] In this embodiment, the parameters of the permanent magnet synchronous motor are shown in Table 1.

[0138] Table 1 Parameters of Permanent Magnet Synchronous Motor

[0139]

[0140]

[0141] The simulation conditions are set as follows. The permanent magnet synchronous motor is in no-load operation mode. During the simulation, the speed of the motor will increase from the initial 0 r / min and finally stabilize at 1000 r / min.

[0142] The simulation parameters are set as follows, m = 135, n = 325, σ = 0.9, β = 1.5, K smop = 636.6, K smoi = 202500, k = 0.8, ω = 408.4.

[0143] From Figure 10It can be seen that Figure 10 (a) shows the back electromotive force waveform observed by the traditional sliding mode observer, Figure 10 (c) is its corresponding Lissajous figure of the back electromotive force. From these two figures, it can be found that the back electromotive force signal contains high-frequency noise components, which will have an adverse impact on the accurate observation of the rotor position. And Figure 10 (b) presents the back electromotive force waveform observed by the improved full-order sliding mode observer, Figure 10 (d) is its Lissajous figure of the back electromotive force. It can be seen from these two figures that the improved full-order sliding mode observer can effectively filter out the high-frequency noise in the back electromotive force signal, thus significantly improving the observation accuracy of the rotor position.

[0144] From Figure 11 it can be seen that the SMO with angle compensation cannot accurately track the actual position of the rotor in the initial stage, while the improved full-order sliding mode observer (improved FSMO) can track the actual position of the rotor well. In addition, the improved full-order sliding mode observer can well fit the curve of the actual rotor position, while the SMO with angle compensation has a certain degree of deviation.

[0145] From Figure 12 it can be seen that the error of the improved full-order sliding mode observer (improved FSMO) in the initial stage is less than that of the SMO with angle compensation, and there is no large error fluctuation. In the subsequent stable stage, the error of the improved FSMO is also much lower than that of the SMO with angle compensation. This shows that the improved full-order sliding mode observer based on SOGI-QNPLL can accurately extract the rotor position and significantly improve the observation accuracy.

Claims

1. A sensorless vector control method for a permanent magnet synchronous motor based on SOGI-QNPLL, characterized in that: It includes the following steps: Step 1, construct the current state equation of the permanent magnet synchronous motor in the two-phase stationary coordinate system; Step 2, construct a new switching function, and design an improved full-order sliding mode observer according to the new switching function and the current state equation; Step 3, analyze the convergence of the improved full-order sliding mode observer, and calculate the value ranges of the gains m and n of the improved full-order sliding mode observer; Step 4, analyze the improved full-order sliding mode observer, and discretize the improved full-order sliding mode observer by using the forward Euler method; Step 5, build a phase-locked loop, perform normalized design on the phase-locked loop, and build a normalized phase-locked loop; Step 6, build a second-order generalized integrator and discretize it by using the bilinear transformation method, combine the discrete SOGI and QNPLL to form SOGI-QNPLL, and use it to estimate the rotor position.

2. The sensorless vector control method for a permanent magnet synchronous motor based on SOGI-QNPLL according to claim 1, characterized in that: In the above-mentioned step 1, the current state equation of the permanent magnet synchronous motor in the two-phase stationary coordinate system is In the formula, u α , u β are the voltages on the α-axis and β-axis respectively, i α , i β are the currents on the α-axis and β-axis respectively, L d , L q are the d-axis and q-axis inductances respectively, R s is the stator resistance, ω e is the electrical angular velocity, E α , E β are the extended back electromotive forces; The extended back electromotive force in the said step 1 is In the formula, θ e is the electrical angle of the rotor position, and ψ f is the magnetic flux linkage of the permanent magnet.

3. The sensorless vector control method for a permanent magnet synchronous motor based on SOGI-QNPLL according to claim 1, characterized in that: The new switching function in step 2 described above is where sign(s) is the sign function, σ represents the boundary layer thickness of the function fanp(s), and 0 < σ < 1, β > 1; In the said step 2, the improved full-order sliding mode observer is In the formula,[[]] where is the observed value of the stator current,[[]] where is the observed value of the extended back electromotive force,[[]] B = -L d ·I,[[]] D = 1 / L d ·I,[[]] is the observed electrical angular velocity, u s =[u α u β T ,[[]] K is the feedback gain matrix, m and n are the gains of the improved full-order sliding mode observer,[[]] fanp(s) is the new switching function proposed by the present invention.[[]]​ 4. The sensorless vector control method for a permanent magnet synchronous motor based on SOGI-QNPLL according to claim 1, characterized in that: In the above step 3, in order to ensure the asymptotic stability of the improved full-order sliding mode observer, the condition that the gain m of the improved full-order sliding mode observer must satisfy is In the formula,[[]]END]] is the current observation error, and satisfies is the extended back electromotive force observation error, and satisfies In step 3, in order to ensure the asymptotic stability of the improved full-order sliding mode observer, the condition that the gain n of the improved full-order sliding mode observer must satisfy is where L is the inductance of the permanent magnet synchronous motor, and it satisfies L = L d = L q , is the observed error of the electrical angular velocity, and it satisfies 5. The sensorless vector control method for a permanent magnet synchronous motor based on SOGI-QNPLL according to claim 1, characterized in that: The back electromotive force observed in the said step 4 can be expressed as In the formula, This term represents It has the characteristics of a second-order low-pass filter, which can filter out the high-frequency noise of the system, so there is no need to use a low-pass filter for filtering, thus avoiding the problems of phase lag and back electromotive force amplitude attenuation caused by the use of a low-pass filter; The formula of the discretized improved full-order sliding mode observer in step 4 is where T s is the sampling time, is the value of the observed current at the current moment, is the value of the observed current at the next moment, 6. The sensorless vector control method for a permanent magnet synchronous motor based on SOGI-QNPLL according to claim 1, characterized in that: In step 5, the transfer function of the PLL is In the formula, is the observed electrical angle of the rotor position, K smop and K smoi are the parameters of the PI regulator; The transfer function of the QNPLL in step 5 described above is In the formula, ω n is the undamped natural oscillation frequency and satisfies The proportionality coefficient is K smop = 2ξω n , ξ is the damping ratio, and the integral coefficient is 7. The sensorless vector control method for a permanent magnet synchronous motor based on SOGI-QNPLL according to claim 1, characterized in that: In step 6, the SOGI closed-loop transfer function is where v is the input signal, v′ and qv′ are the output signals, where v′ has the same phase and amplitude as the fundamental wave of v while qv′ lags by 90°, k affects the bandwidth of the closed-loop system, and ω is the resonance frequency of SOGI; The expression of the discretized SOGI in step 6 described above is In the formula, T s is the sampling time.

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