Double-three-phase PMSG position-sensorless control method under open-circuit fault

Abstract

The invention discloses a dual three-phase PMSG position sensorless control method under an open-circuit fault, and belongs to the technical field of permanent magnet synchronous generator control. The method comprises the following steps: establishing a mathematical model under an alpha-beta coordinate system when an open-circuit fault occurs; establishing a full-order sliding-mode observer when an open-circuit fault occurs; designing a sliding-mode surface; carrying out convergence proving; and demodulating the estimated position and the rotating speed. According to the method, position-sensorless control can still be performed during fault-tolerant control under the DTP-PMSG one-phase open-circuit fault, and stable control under the fault state is realized by constructing a mathematical model and a full-order sliding-mode observer during the open-circuit fault, so that the fault-tolerant performance of the system is greatly enhanced. Due to the characteristic, the DTP-PMSG can still keep high-performance operation when facing a one-phase open-circuit fault, and the requirements of occasions with high reliability requirements on the system are met.

Description

Technical Field

[0001] The invention relates to a dual three-phase PMSG position sensorless control method under an open circuit fault, belonging to the technical field of permanent magnet synchronous generator control. Background Art

[0002] DTP-PMSG (Dual Three-Phase Permanent Magnet Synchronous Generator) has the advantages of high power density, low rated power per phase, and good fault tolerance. Since DTP-PMSG has more control freedom, it can use the extra freedom to achieve fault-tolerant control, which is suitable for applications with high system reliability requirements.

[0003] Similar to the traditional three-phase PMSG sensorless technology, the DTP-PMSG sensorless technology is generally divided into two types: high-frequency injection method and model-based position estimation method. The high-frequency injection method has a certain dependence on the saliency of the motor and is suitable for low-speed operation; the model-based position estimation method estimates the back electromotive force or magnetic flux and is more suitable for medium and high-speed operation.

[0004] In the model-based position estimation method, it is common to use a sliding mode observer to estimate the back EMF, but this method has a jitter problem, which affects the position observation accuracy. In order to solve the jitter problem, the observed back EMF can usually be filtered using a first-order low-pass filter to obtain a smoother back EMF, but this method will cause a phase delay problem.

[0005] There are two main approaches to avoid phase delay and mitigate jitter:

[0006] One is to change the observer into a quasi-sliding mode observer, for example, by using a saturation function;

[0007] The second is to improve the filtering method of estimating back EMF while ensuring the phase margin of the system, such as building a full-order sliding mode observer, filtering out high-frequency harmonics by reasonably setting the feedback gain, and avoiding obvious phase lag.

[0008] Although the current position sensorless control strategies for DTP-PMSG in normal operation are very mature, these strategies cannot be directly applied to DTP-PMSG in the case of open circuit fault. Therefore, how to develop a DTP-PMSG position sensorless control strategy that is suitable for normal operation and can maintain high performance in the case of open circuit fault has become a technical problem that needs to be solved urgently. Summary of the invention

[0009] In order to solve the problems existing in the background technology, the present invention provides a position sensorless control method for a dual three-phase PMSG under an open circuit fault.

[0010] To achieve the above object, the present invention adopts the following technical solution: a dual three-phase PMSG position sensorless control method under an open circuit fault, the method comprising the following steps:

[0011] S1: Establish a mathematical model in the α-β coordinate system for open circuit fault;

[0012] S101: Construct the voltage equation and flux equation of a one-phase open-circuit DTP-PMSG in the natural coordinate system as follows:

[0013]

[0014] ψ 5s =L 5s i 5s +γ 5s ψ f (2)

[0015] In formula (1)-(2):

[0016] ψ f represents the flux linkage of permanent magnet;

[0017] u 5s =[u A u B u C u D u E ] T It represents the phase voltage of DTP-PMSG with one phase open circuit;

[0018] i 5s =[i A i B i C i D i E ] T It represents the phase current of DTP-PMSG with one phase open circuit;

[0019] ψ 5s =[ψ A ψ B ψ C ψ D ψ E ] T It represents the flux linkage of DTP-PMSG with one phase open circuit;

[0020] Represents the flux linkage coefficient matrix, where: θ e Indicates the rotor electrical angle;

[0021] Represents the stator resistance matrix, where: R s It represents the phase resistance of DTP-PMSG with one phase open circuit;

[0022] Represents the stator inductance matrix, where: L0 represents the stator main self-inductance; L aal represents the stator leakage inductance; I5 represents the fifth-order unit matrix;

[0023] S102: Considering that the sum of the currents of phases D and E is 0, the transformation matrix of the dual three-phase motor is deleted and the rows and columns related to phase F are adjusted to obtain the static transformation matrix T when one phase is open. 5 / 5s as follows:

[0024]

[0025] S103: Perform a static transformation on the voltage equation and the flux equation after deleting the F phase row 5 / 5s By static transformation, ignoring the z2-z3 subspace of the zero-sequence component, the voltage equation and magnetic flux equation in the α-β-z1 coordinate system are obtained as follows:

[0026]

[0027] In formula (4)-(5):

[0028] u α Represents the voltage of the α coordinate axis;

[0029] u β represents the voltage of the β axis;

[0030] Represents the voltage of the z1 coordinate axis;

[0031] i α represents the current of the α coordinate axis;

[0032] i β represents the current of the β axis;

[0033] Represents the current of the z1 coordinate axis;

[0034] t represents time;

[0035] ψ α Represents the magnetic flux component of the α coordinate axis;

[0036] ψ β Represents the magnetic flux component of the β coordinate axis;

[0037] Represents the magnetic flux component of the z1 coordinate axis;

[0038] L α =3L0+L aal represents the inductance of the α coordinate axis;

[0039] represents the inductance of the β coordinate axis;

[0040] S104: Combining equation (4) and equation (5) to obtain the voltage equation including the back electromotive force:

[0041]

[0042] In formula (6):

[0043] Respectively represent the back electromotive force components of the α coordinate axis and the β coordinate axis, where ω e Represents the rotor electrical angular frequency.

[0044] S2: Establish a full-order sliding mode observer for open circuit fault:

[0045] S201: The mathematical model obtained in S1 is written as a full-order state equation with stator current and back electromotive force as state variables as follows:

[0046]

[0047] S202: Based on the full-order state equation, ignoring the z1-axis space that does not contain position information, a full-order sliding mode observer is constructed as follows:

[0048]

[0049] In formula (8):

[0050] represents the estimated value of the current on the α axis;

[0051] represents the estimated value of the current on the β axis;

[0052] represents the estimated value of the back electromotive force component of the α coordinate axis;

[0053] represents the estimated value of the back-EMF component of the β coordinate axis;

[0054] represents the estimated value of the rotor electrical angular frequency;

[0055] m represents the back-EMF gain in the observer;

[0056] They represent the sliding mode control functions of the α coordinate axis and the β coordinate axis respectively, where: k represents the sliding mode gain; sgn() represents the sign function.

[0057] S3: Design sliding surface;

[0058] S301: Select sliding surface s(x) based on stator current error:

[0059]

[0060] In formula (9):

[0061] represents the current estimation error of the α coordinate axis;

[0062] represents the current estimation error of the β axis;

[0063] S302: Substitute equation (7) and equation (8) into α and i β Subtract the two lines and get the current observation error state equation as follows:

[0064]

[0065] In formula (10):

[0066] represents the back EMF estimation error of the α coordinate axis;

[0067] Represents the back EMF estimation error of the β coordinate axis.

[0068] S4: Prove convergence;

[0069] S401: Perform stability analysis on the sliding mode observer and define the Lyapunov function V as follows:

[0070]

[0071] In formula (11):

[0072] s represents the sliding surface;

[0073] S402: Derivation of the Lyapunov function:

[0074]

[0075] S403: When the sliding mode gain When , the Lyapunov function stability condition is achieved

[0076] S404: When the existence condition of the sliding mode is met, the current estimation value converges to the actual current value, and the back electromotive force observation error is expressed as:

[0077]

[0078] S405: Substitute e in equation (7) and equation (8) α and e β Subtract the two lines and get the back EMF observation error state equation as follows:

[0079]

[0080] S406: Solve the differential equation system, whose characteristic equation is as follows:

[0081]

[0082] In formula (15):

[0083] p represents a complex frequency domain variable;

[0084] S407: Convergence of back-EMF observation error:

[0085] when When , the characteristic root is:

[0086]

[0087] In formula (16):

[0088] j represents the imaginary unit;

[0089] At this time, the characteristic roots of the characteristic equation are a pair of conjugate complex roots with a negative real part, and the back-EMF observation error converges; within this range, the larger the back-EMF gain m, the farther the characteristic root is from the imaginary axis, and the faster the back-EMF observation error converges;

[0090] when When , the characteristic root is:

[0091]

[0092] Since the square root part is less than 1, and L α +L β >L α -L β >0, at this time the characteristic roots of the characteristic equation are a pair of negative real roots, and the back-EMF observation error converges; and the larger the back-EMF gain m, the farther the characteristic roots are from the imaginary axis, and the faster the back-EMF observation error converges.

[0093] S5: Demodulation estimated position and speed:

[0094] The observed back EMF is input into the modified phase-locked loop to obtain the estimated position and speed, completing the position sensorless control of the DTP-PMSG under a one-phase open-circuit fault.

[0095] Compared with the prior art, the present invention has the following beneficial effects:

[0096] 1. The present invention can still perform position sensorless control during fault-tolerant control under a single-phase open-circuit fault of the DTP-PMSG. By constructing a mathematical model and a full-order sliding mode observer for an open-circuit fault, stable control under a fault state is achieved, thereby greatly enhancing the fault-tolerant performance of the system. This feature enables the DTP-PMSG to maintain high-performance operation when facing a single-phase open-circuit fault, meeting the needs of occasions with high system reliability requirements.

[0097] 2. The control method of the present invention is completely software-based and can be run on a standard digital control chip (such as DSP or FPGA). Therefore, no additional hardware changes are required to achieve position sensorless control of the DTP-PMSG under open circuit fault. This feature reduces the cost of system upgrades and maintenance and improves the flexibility and scalability of the system.

[0098] 3. The method proposed in the present invention is not only applicable to complex control systems, but can also be easily integrated into basic dual three-phase PWM rectification systems. This means that even without complex hardware support, the system can achieve efficient and stable single-phase open circuit fault tolerance control.

[0099] 4. The present invention can achieve accurate estimation of back electromotive force by constructing a full-order sliding mode observer and designing a reasonable sliding mode surface. In this process, by optimizing the filtering method and feedback gain setting, phase delay and jitter problems are effectively avoided, thereby improving the accuracy and stability of position estimation.

[0100] 5. The present invention can obtain the estimated position and speed information of the DTP-PMSG in real time by inputting the observed back electromotive force into the modified phase-locked loop, which helps to improve the overall performance and stability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] Figure 1 This is a schematic diagram of the connection method when one phase is open circuit fault;

[0102] Figure 2 It is the principle block diagram of the adjusted normalized phase-locked loop during open circuit fault tolerance control;

[0103] Figure 3 The steady-state experimental result diagram obtained by using the method of the present invention, wherein: (a) is the observed back electromotive force result diagram; (b) is the estimated error result diagram between the actual position and the estimated position;

[0104] Figure 4It is an experimental result diagram of a DC given voltage variation experiment using the method of the present invention, wherein the DC side given voltage is reduced from a rated 50V to 40V, and then increased from 40V back to the rated 50V;

[0105] Figure 5 is an experimental result diagram of a load sudden change experiment using the method of the present invention, wherein the load is suddenly reduced from a rated 150Ω to no-load, and then suddenly increased from no-load back to a rated 150Ω load;

[0106] Figure 6 It is a graph of experimental results of a speed mutation experiment using the method of the present invention, wherein the original engine speed is suddenly increased from 600 r / min to 800 r / min, and then suddenly reduced from 800 r / min back to 600 r / min. DETAILED DESCRIPTION

[0107] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0108] A dual three-phase PMSG position sensorless control method under an open circuit fault, the method comprising the following steps:

[0109] S1: Establish a mathematical model in the α-β coordinate system for open circuit fault;

[0110] S101: Construct the voltage equation and flux equation of a one-phase open-circuit DTP-PMSG in the natural coordinate system as follows:

[0111]

[0112] ψ 5s =L 5s i 5s +γ 5s ψ f (2)

[0113] In formula (1)-(2):

[0114] ψ f represents the flux linkage of permanent magnet;

[0115] u 5s =[u A u B u C u D u E ] TIt represents the phase voltage of DTP-PMSG with one phase open circuit;

[0116] i 5s =[i A i B i C i D i E ] T It represents the phase current of DTP-PMSG with one phase open circuit;

[0117] ψ 5s =[ψ A ψ B ψ C ψ D ψ E ] T It represents the flux linkage of DTP-PMSG with one phase open circuit;

[0118] Represents the flux linkage coefficient matrix, where: θ e Indicates the rotor electrical angle;

[0119] Represents the stator resistance matrix, where: R s It represents the phase resistance of DTP-PMSG with one phase open circuit;

[0120] Represents the stator inductance matrix, where: L0 represents the stator main self-inductance; L aal represents the stator leakage inductance; I5 represents the fifth-order unit matrix;

[0121] S102: Considering that the sum of the currents of phases D and E is 0, the transformation matrix of the dual three-phase motor is deleted and the rows and columns related to phase F are adjusted to obtain the static transformation matrix T when one phase is open. 5 / 5s as follows:

[0122]

[0123] S103: Perform a static transformation on the voltage equation and the flux equation after deleting the F phase row 5 / 5s By static transformation, ignoring the z2-z3 subspace of the zero-sequence component, the voltage equation and magnetic flux equation in the α-β-z1 coordinate system are obtained as follows:

[0124]

[0125] In formula (4)-(5):

[0126] u α Represents the voltage of the α coordinate axis;

[0127] u β represents the voltage of the β axis;

[0128] Represents the voltage of the z1 coordinate axis;

[0129] i α represents the current of the α coordinate axis;

[0130] i β represents the current of the β axis;

[0131] Represents the current of the z1 coordinate axis;

[0132] t represents time;

[0133] ψ α Represents the magnetic flux component of the α coordinate axis;

[0134] ψ β Represents the magnetic flux component of the β coordinate axis;

[0135] Represents the magnetic flux component of the z1 coordinate axis;

[0136] L α =3L0+L aal represents the inductance of the α coordinate axis;

[0137] represents the inductance of the β coordinate axis;

[0138] S104: Combining equation (4) and equation (5) to obtain the voltage equation including the back electromotive force:

[0139]

[0140] In formula (6):

[0141] Respectively represent the back electromotive force components of the α coordinate axis and the β coordinate axis, where ω e Represents the rotor electrical angular frequency.

[0142] S2: Establish a full-order sliding mode observer for open circuit fault:

[0143] S201: The mathematical model obtained in S1 is written as a full-order state equation with stator current and back electromotive force as state variables as follows:

[0144]

[0145] S202: Based on the full-order state equation, ignoring the z1-axis space that does not contain position information, a full-order sliding mode observer is constructed as follows:

[0146]

[0147] In formula (8):

[0148] represents the estimated value of the current on the α axis;

[0149] represents the estimated value of the current on the β axis;

[0150] represents the estimated value of the back electromotive force component of the α coordinate axis;

[0151] represents the estimated value of the back-EMF component of the β coordinate axis;

[0152] represents the estimated value of the rotor electrical angular frequency;

[0153] m represents the back-EMF gain in the observer;

[0154] They represent the sliding mode control functions of the α coordinate axis and the β coordinate axis respectively, where: k represents the sliding mode gain; sgn() represents the sign function.

[0155] S3: Design sliding surface;

[0156] S301: Select sliding surface s(x) based on stator current error:

[0157]

[0158] In formula (9):

[0159] represents the current estimation error of the α coordinate axis;

[0160] represents the current estimation error of the β coordinate axis;

[0161] S302: Substitute equation (7) and equation (8) into α and i β Subtract the two lines and get the current observation error state equation as follows:

[0162]

[0163] In formula (10):

[0164] represents the back EMF estimation error of the α coordinate axis;

[0165] Represents the back EMF estimation error of the β coordinate axis.

[0166] S4: Prove convergence;

[0167] S401: Perform stability analysis on the sliding mode observer and define the Lyapunov function V as follows:

[0168]

[0169] In formula (11):

[0170] s represents the sliding surface, that is, formula (9);

[0171] S402: Derivation of the Lyapunov function:

[0172]

[0173] S403: When the sliding mode gain When , the Lyapunov function stability condition is achieved

[0174] S404: When the existence condition of the sliding mode is met, the current estimation value converges to the actual current value, and the back electromotive force observation error is expressed as:

[0175]

[0176] S405: Substitute e in equation (7) and equation (8) α and e β Subtract the two lines and get the back EMF observation error state equation as follows:

[0177]

[0178] S406: Solve the differential equation system, whose characteristic equation is as follows:

[0179]

[0180] In formula (15):

[0181] p represents a complex frequency domain variable;

[0182] S407: Convergence of back-EMF observation error:

[0183] when When , the characteristic root is:

[0184]

[0185] In formula (16):

[0186] j represents the imaginary unit;

[0187] At this time, the characteristic roots of the characteristic equation are a pair of conjugate complex roots with a negative real part, and the back-EMF observation error converges; within this range, the larger the back-EMF gain m, the farther the characteristic root is from the imaginary axis, and the faster the back-EMF observation error converges;

[0188] when When , the characteristic root is:

[0189]

[0190] Since the square root part is less than 1, and L α +L β >L α -L β >0, at this time the characteristic roots of the characteristic equation are a pair of negative real roots, and the back-EMF observation error converges; and the larger the back-EMF gain m, the farther the characteristic roots are from the imaginary axis, and the faster the back-EMF observation error converges.

[0191] S5: Demodulation estimated position and speed:

[0192] Under the premise of meeting the convergence conditions, the observer can be guaranteed to converge. However, due to the open circuit fault, the back EMF components of the α-axis and the β-axis are inconsistent. The estimated back EMF amplitude of the input phase-locked loop and the normalization process can be corrected, such as Figure 2 As shown. By inputting the observed back EMF into the modified phase-locked loop, the estimated position and speed can be obtained, thus completing the position sensorless control of the DTP-PMSG under a single-phase open-circuit fault.

[0193] Embodiment 1:

[0194] When one phase of the DTP-PMSG in the present invention is open, take the F phase open as an example, the connection diagram is as follows Figure 1 As shown. The parameters of the dual three-phase PWM rectification system in the experiment are as follows:

[0195] The rated speed of the motor is 600r / min, the number of pole pairs is 5, the inductance of the d-axis and q-axis is 8mH, the leakage inductance is 0.8mH, the phase resistance is 0.8Ω, the permanent magnet flux is 0.03779wb, the rated voltage of the DC side is 50V, the load resistance is 150Ω, and the filter capacitor is 660μF. The sliding mode gain k in the sliding mode observer is 5, and the back electromotive force gain m is 200. The back electromotive force observation results are as follows Figure 3 As shown in (a), the observed α-axis back EMF amplitude is 11.85V, and the β-axis back EMF amplitude is 5.94V. The α-axis back EMF amplitude is twice that of the β-axis back EMF amplitude, and the phase difference is still 90°, which is consistent with the theory. The α-axis back EMF and β-axis back EMF waveforms are smooth and have no obvious phase lag. The position estimation result obtained by normalized phase-locked loop demodulation is shown in Figure 3As shown in (b), the maximum error of the position signal estimation is 0.11 rad, which has a high steady-state accuracy. When the DC given voltage decreases and increases, the error of the position signal estimation will increase slightly, with the maximum errors being 0.23 rad and 0.2 rad respectively; when the load decreases and increases suddenly, the error of the position signal estimation will increase slightly, with the maximum errors being 0.19 rad and 0.24 rad respectively; when the speed increases and decreases suddenly, the error of the position signal estimation will increase significantly, with the maximum errors being 0.42 rad and 0.61 rad respectively; after the dynamic response ends, the position estimation error can return to a smaller value.

[0196] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations within the meaning and range of equivalents of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0197] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A dual three-phase PMSG position sensorless control method under open circuit fault, characterized by: The method comprises the following steps: S1: Establish a mathematical model in the α-β coordinate system for open circuit fault; S2: Establish a full-order sliding mode observer for open circuit fault: S3: Design sliding surface; S4: Prove convergence; S5: Demodulation estimated position and speed: The observed back EMF is input into the modified phase-locked loop to obtain the estimated position and speed, completing the position sensorless control of the DTP-PMSG under a one-phase open-circuit fault.

2. The dual three-phase PMSG position sensorless control method under an open circuit fault according to claim 1, characterized in that: The S1 comprises the following steps: S101: Construct the voltage equation and flux equation of a one-phase open-circuit DTP-PMSG in the natural coordinate system as follows: ψ 5s =L 5s I 5s +g 5s ψ f (2) In formula (1)-(2): ψ f represents the flux linkage of permanent magnet; u 5s =[u A u B u C u D u E ] T It represents the phase voltage of DTP-PMSG with one phase open circuit; i 5s =[i A i B i C i D i E ] T It represents the phase current of DTP-PMSG with one phase open circuit; ψ 5s =[ψ A ψ B ψ C ψ D ψ E ] T It represents the flux linkage of DTP-PMSG with one phase open circuit; Represents the flux linkage coefficient matrix, where: θ e Indicates the rotor electrical angle; Represents the stator resistance matrix, where: R s It represents the phase resistance of DTP-PMSG with one phase open circuit; Represents the stator inductance matrix, where: L0 represents the stator main self-inductance; L aal represents the stator leakage inductance; I5 represents the fifth-order unit matrix; S102: Considering that the sum of the currents of phases D and E is 0, the transformation matrix of the dual three-phase motor is deleted and the rows and columns related to phase F are adjusted to obtain the static transformation matrix T when one phase is open circuit. 5 / 5s as follows: S103: Perform a static transformation on the voltage equation and the flux equation after deleting the F phase row 5 / 5s By static transformation, ignoring the z2-z3 subspace of the zero-sequence component, the voltage equation and magnetic flux equation in the α-β-z1 coordinate system are obtained as follows: In formula (4)-(5): u α Represents the voltage of the α coordinate axis; u β represents the voltage of the β axis; Represents the voltage of the z1 coordinate axis; i α represents the current of the α coordinate axis; i β represents the current of the β axis; Represents the current of the z1 coordinate axis; t represents time; ψ α Represents the magnetic flux component of the α coordinate axis; ψ β Represents the magnetic flux component of the β coordinate axis; Represents the magnetic flux component of the z1 coordinate axis; L α =3L0+L aal represents the inductance of the α coordinate axis; represents the inductance of the β coordinate axis; S104: Combining equation (4) and equation (5) to obtain the voltage equation including the back electromotive force: In formula (6): Respectively represent the back electromotive force components of the α coordinate axis and the β coordinate axis, where ω e Represents the rotor electrical angular frequency.

3. The dual three-phase PMSG position sensorless control method under an open circuit fault according to claim 2 is characterized in that: The S2 comprises the following steps: S201: The mathematical model obtained in S1 is written as a full-order state equation with stator current and back electromotive force as state variables as follows: S202: Based on the full-order state equation, ignoring the z1-axis space that does not contain position information, a full-order sliding mode observer is constructed as follows: In formula (8): represents the estimated value of the current on the α axis; represents the estimated value of the current on the β axis; represents the estimated value of the back electromotive force component of the α coordinate axis; represents the estimated value of the back electromotive force component of the β coordinate axis; represents the estimated value of the rotor electrical angular frequency; m represents the back-EMF gain in the observer; They represent the sliding mode control functions of the α coordinate axis and the β coordinate axis respectively, where: k represents the sliding mode gain; sgn() represents the sign function.

4. The dual three-phase PMSG position sensorless control method under an open circuit fault according to claim 3 is characterized in that: The S3 comprises the following steps: S301: Select sliding surface s(x) based on stator current error: In formula (9): represents the current estimation error of the α coordinate axis; represents the current estimation error of the β coordinate axis; S302: Substitute equation (7) and equation (8) into α and i β Subtract the two lines and get the current observation error state equation as follows: In formula (10): represents the back EMF estimation error of the α coordinate axis; Represents the back EMF estimation error of the β coordinate axis.

5. The dual three-phase PMSG position sensorless control method under an open circuit fault according to claim 4, characterized in that: The S4 comprises the following steps: S401: Perform stability analysis on the sliding mode observer and define the Lyapunov function V as follows: In formula (11): s represents the sliding surface; S402: Derivation of the Lyapunov function: S403: When the sliding mode gain When , the Lyapunov function stability condition is achieved S404: When the existence condition of the sliding mode is met, the current estimation value converges to the actual current value, and the back electromotive force observation error is expressed as: S405: Substitute e in equation (7) and equation (8) α and e β Subtract the two lines and get the back EMF observation error state equation as follows: S406: Solve the differential equations, Its characteristic equation is as follows: In formula (15): p represents a complex frequency domain variable; S407: Convergence of back-EMF observation error: when When , the characteristic root is: In formula (16): j represents the imaginary unit; At this time, the characteristic roots of the characteristic equation are a pair of conjugate complex roots with a negative real part, and the back-EMF observation error converges; within this range, the larger the back-EMF gain m, the farther the characteristic root is from the imaginary axis, and the faster the back-EMF observation error converges; when When , the characteristic root is: Since the square root part is less than 1, and L α +L β >L α -L β >0, at this time the characteristic roots of the characteristic equation are a pair of negative real roots, and the back-EMF observation error converges; and the larger the back-EMF gain m, the farther the characteristic roots are from the imaginary axis, and the faster the back-EMF observation error converges.

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