Optimization Control Method of Permanent Magnet Linear Generator Applied to Single-Degree-of-Freedom Direct-Drive Wave Energy Generation System

Abstract

The present invention discloses an optimized control method for a permanent magnet linear generator applied to a single-degree-of-freedom direct-drive wave energy power generation system, which relates to the field of permanent magnet linear generators for wave energy power generation and is mainly used for energy conversion and efficiency improvement of wave energy power generation devices. The invention includes the following steps: S1, establishment of a mathematical model of the permanent magnet linear generator; S2, establishment of a mathematical model of the maximum wave energy capture condition; S3, parameter setting and optimized control method of the permanent magnet linear generator; the present invention improves the operation stability and power generation conversion efficiency of the motor by optimizing the structure and control method of the linear motor.

Description

Technical Field

[0001] The present invention relates to the technical field of single-degree-of-freedom direct-drive wave energy power generation, and specifically to an optimized control method for a permanent magnet linear generator applied to a single-degree-of-freedom direct-drive wave energy power generation system. Background Technique

[0002] Permanent magnet linear generators have the advantages of simple structure, reliable operation, high efficiency, etc., which makes them have broad application prospects in the field of wave energy power generation. The environment for wave energy power generation is the ocean, and its environmental conditions are complex and changeable, including the influence of various factors such as wind waves, ocean currents, and tides. This environment may cause the permanent magnet linear motor to be subjected to large impacts and vibrations during operation, affecting its stability and reliability. Due to the instability, randomness, and intermittency of wave energy, etc., the operation process of the permanent magnet linear generator faces complex dynamic characteristics and non-linear characteristics, resulting in unstable power generation operation performance, and further affecting the wave energy power generation conversion efficiency, which poses a challenge to the optimized control of the permanent magnet linear generator.

[0003] To solve the deficiencies mentioned in the above background technique, the purpose of the present invention is to provide an optimized control method for the motor applied to a single-degree-of-freedom direct-drive wave energy power generation system. This optimized control method aims to reduce the losses of the motor and improve the operation efficiency and stability of the motor by optimizing the structural design and operation parameters of the motor. Summary of the Invention

[0004] The purpose of the present invention can be achieved through the following technical solutions. An optimized control method for the motor applied to a single-degree-of-freedom direct-drive wave energy power generation system, the method includes the following steps:

[0005] S1. Establishment of the mathematical model of the permanent magnet linear generator

[0006] S2. Establishment of the mathematical model of the maximum wave energy capture condition

[0007] S3. Parameter setting and optimized control experimental method of the permanent magnet linear generator

[0008] The establishment of the mathematical model of the permanent magnet linear generator includes the following steps:

[0009] The permanent magnet synchronous linear motor (PMSLG) can be mathematically modeled by imitating the permanent magnet synchronous motor (PMSG). The stator windings are symmetrically distributed in three phases, and the axes of each winding differ by 120° electrical angle; the air-gap magnetomotive force and magnetic flux density generated are sinusoidally distributed; the influence of ventilation grooves and winding slots is ignored, and it is assumed that the surfaces of the stator and rotor are smooth; the influence of magnetic circuit saturation, hysteresis loss, and eddy current loss is ignored;

[0010] Perform the Park transformation to transform the electromagnetic quantities represented in the stationary three-phase coordinate system a, b, c into electromagnetic quantities represented in the two-phase rectangular coordinate system d, q rotating with the rotor and the stationary 0-axis coordinate system (collectively referred to as the dq0 coordinate system). The coordinate transformation does not change the internal electromagnetic relationship of the generator.

[0011] The Park transformation transforms the variable-coefficient differential equation into a constant-coefficient differential equation. The Park transformation with equal power has the function:

[0012]

[0013] In the three-phase stationary coordinate system, the voltage function of the PMSG stator three-phase circuit is:

[0014]

[0015] Where R a , R b , R c are the three-phase resistances. Also, because the three-phase windings are symmetric, so R a =R b =R c =R s ; i a , i b , i c are the stator three-phase currents; φ a , φ b , φ c are the three-phase stator fluxes. The corresponding flux functions are:

[0016]

[0017] Where L is the self-inductance and they are all equal; M is the mutual inductance and they are all equal; φ f is the permanent magnet flux; θ is the angle between the d-axis and the a-axis, θ = ω e t; ω e is the electrical angular velocity, n p is the number of pole pairs of the motor, and τ is the pole pitch of the motor. After the equal-power Park transformation, the voltage functions in the dq-axis rotating coordinate system are:

[0018]

[0019] u d , u q , i d , i q are the dq-axis stator voltages and currents respectively; L d , L q are the dq-axis equivalent inductances respectively, L d =L q =Ls ; Ψ d 、Ψ q is the equivalent flux linkage of the stator flux linkage under the dq axes. The equivalent flux linkage function is:

[0020]

[0021] From the above formulas, the complete expressions of the voltage functions of the permanent magnet synchronous generator under the d and q coordinate axes can be obtained:

[0022]

[0023] Through the above formulas, the SVPWM control of the generator based on i d = 0 can be achieved.

[0024] The electromagnetic force F of the generator pto can be obtained by analogy with the electromagnetic force of the motor, and its functional form is:

[0025]

[0026] Because i d = 0, L d = L q = L s , the simplified function is:

[0027]

[0028] The induced electromotive force E of the PTO device is:

[0029]

[0030] The stator voltage u is the voltage difference between the output voltage U and the induced electromotive force E of the PTO device, which is:

[0031]

[0032] Furthermore, the establishment of the maximum wave energy capture condition includes the following steps:

[0033] Float dynamics function:

[0034] Z b is the displacement of the float body relative to the hydrological zero point; is the acceleration of the float body

[0035] M b is the total mass of the float body and the mover of the linear generator

[0036] F e is the wave force

[0037] F hsIs the still water restoring force: F hs =-K hs ·Z b

[0038] K hs Is the equivalent elastic coefficient of seawater, which is related to the geometric structure of the float body

[0039] F pto Is the thrust of the PTO device, that is, the electromagnetic thrust of the linear motor

[0040] F rad Is the radiation force received by the float body

[0041] According to the study of wave forces, under irregular waves, the convolution integral formula of the Cummins equation is introduced to describe the fluid memory effect, and the corresponding radiation force function:

[0042]

[0043] After organizing the above formula, the dynamic equation of the single-degree-of-freedom direct-drive wave power generation device can be obtained:

[0044]

[0045] Furthermore, the frequency-domain equation of the direct-drive wave power generation system is obtained:

[0046]

[0047] In the formula, F g Is the counter-electromagnetic force, which is the interaction force of the electromagnetic thrust F pto ; B0 is the radiation force damping coefficient, which can be obtained from the above formula:

[0048]

[0049] When the counter-electromagnetic force of the direct-drive wave energy generation system is only linearly related to the velocity of the float body, it can be expressed as:

[0050]

[0051] In the formula, R e Is the optimal damping coefficient of the direct-drive wave energy generation system.

[0052] The angle θ, R e Between the wave and the velocity of the float body, and ω can be expressed as:

[0053]

[0054] After Laplace transform, it can be obtained:

[0055]

[0056] When the damping Z of the energy output system e is equal to the conjugate of the internal impedance Z1 of the wave energy conversion system, the maximum wave energy capture condition can be obtained:

[0057]

[0058] The optimal speed of the buoy body is obtained as:

[0059]

[0060] The system dynamic model can be equivalent to a second-order resonant circuit, and the response form of the system can be compared to series resonance.

[0061] Under the condition that the device achieves the maximum wave energy capture, as long as it is within the allowable range of the motion stroke, acting force, and output power of the permanent magnet linear generator of the wave energy power generation device, resonance can be achieved in any sea wave energy environment, so that the device can capture the maximum wave energy, and its application area is wide. In the operation of PMLG, energy often undergoes two-way transfer. When the energy flows forward, the motor outputs electrical energy as a generator; conversely, when electrical energy is input, it acts as a motor to input energy to the PTO.

[0062] Furthermore, the experimental method for parameter setting and optimal control of the permanent magnet linear generator includes the following steps:

[0063] Furthermore, for the selection of the primary and secondary structures, the permanent magnet of the long secondary structure is longer than the stator winding. Although more permanent magnet materials are used, the entire stator winding is an effective winding, with high energy conversion efficiency. From the perspective of high-efficiency energy conversion, the long secondary structure is selected for research in this paper.

[0064] Furthermore, for parameter selection, the buoy body of the direct-drive PTO device is connected to the mover of the linear motor through a connecting rod. Driven by the wave force, the buoy body moves to drive the mover of the linear motor to perform vertical heaving motion. Under ideal conditions, the motion equation of the wave can be described as:

[0065]

[0066] H is the wave height and λ is the wavelength. When the sea wave level is grade 4, H = 2.5m and λ = 30m. Under ideal conditions (ignoring factors such as motor friction and wave reflection, φ = 0), the motion speed equation of the wave can be expressed as:

[0067] v = 0.26sin0.21t

[0068] From the above formula, the maximum motion speed of the wave is 0.26m / s. For the convenience of data processing without losing the verification of the motor performance, a constant speed of 0.26m / s is given to the mover, and an optimal control experiment analysis is carried out on the linear generator.

[0069] Furthermore, the permanent magnet linear motor has 9 poles and 12 slots, with m = 3. The modeled linear generator is the same as the long secondary model. Since the linear generator model is completely symmetric left and right, for convenience of analysis, only the right side is modeled here. The motor is designed as a three-phase permanent magnet linear motor, and the label groups of the windings of phases A, B, and C are set.

[0070] Furthermore, the presence or absence of the auxiliary slot structure causes a significant difference in the magnetic flux distribution at the stator end. The auxiliary slot can convert a part of the leakage magnetic flux into effective magnetic flux, greatly reducing the change rate of the air-gap magnetic resistance, and theoretically reducing the detent force on the mover. To reduce the detent force on the mover, the stator structure described above is improved, and the end teeth and slots are widened, which is equivalent to the function of an auxiliary slot.

[0071] Furthermore, compared with before the motor improvement, the amplitude of the no-load induced electromotive force of the linear motor without the auxiliary slot has increased; the difference in the induced electromotive force between phase C and phases A and B has decreased. It is proved that after adding the auxiliary slot, the electromechanical energy conversion efficiency of the linear motor is enhanced under the same conditions, and the working efficiency and performance of the motor have been improved, verifying the correctness and rationality of the improvement of the stator tooth and slot structure of the linear motor.

[0072] Furthermore, when the linear motor is loaded, the load-induced electromotive forces of the three phases are different from each other and are smaller than those in the no-load case. This is jointly caused by the inherent longitudinal end effect of the linear motor and the armature reaction under load conditions. And compared with the no-load induced electromotive force, the phase of each phase is shifted. This is because the phase of the no-load induced electromotive force is only determined by the magnetic field generated by the permanent magnet, while under load it is determined by the magnetic field jointly generated by the permanent magnet and the armature reaction.

[0073] Furthermore, the initial movement direction of the test mover is downward. At time 0, the mover of the linear motor is at the highest position, and then the mover starts to move downward with an increasing speed. At 0.5 s, the speed of the mover reaches the maximum of 0.26 m / s. At this time, the no-load induced electromotive force generated by the stator winding also reaches the maximum. After that, the mover continues to move downward, but the speed gradually decreases, and the amplitude of the induced electromotive force also gradually decreases. When the mover reaches the lowest point at 1 s, the speed of the mover is 0, and the induced electromotive force is also 0. Subsequently, the mover moves upward following the wave, and the changes in its induced electromotive force and speed are similar to those when the mover moves downward.

[0074] Advantages of the present invention: For the linear motor with the improved stator teeth and slots, the mover will be subjected to a smaller detent force during movement. Under no-load and load conditions, the three-phase windings of the linear motor mover can generate induced electromotive forces at constant speed and sinusoidal speed, and the changes in the amplitude and phase of the induced electromotive force are all reasonable, proving the correctness and rationality of the structural design of this linear motor, and further realizing the high-efficiency conversion of wave energy into electrical energy. Description of the Drawings

[0075] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. For those skilled in the art, without creative efforts, other drawings can also be obtained based on these drawings:

[0076] Figure 1 This is the long-secondary linear motor model of the present invention patent;

[0077] Figure 2 This is the winding label group setting of the present invention patent;

[0078] Figure 3 This is the schematic diagram of the magnetic field line distribution of the present invention patent without an auxiliary slot and with an auxiliary slot;

[0079] Figure 4 This is the linear motor model with an auxiliary slot of the present invention patent;

[0080] Figure 5 This is the experimental waveform diagram of the positioning driving force of the present invention patent;

[0081] Figure 6 This is the experimental waveform diagram of the no-load induced electromotive force of the present invention patent;

[0082] Figure 7 This is the experimental waveform diagram of the resistive load induced electromotive force of the present invention patent;

[0083] Figure 8 This is the experimental waveform diagram of the no-load induced electromotive force under sinusoidal speed of the present invention patent;

[0084] Figure 9 This is the experimental curve diagram of the mover speed and position of the present invention patent;

[0085] According to the actual situation, the present invention will be further described in detail below with specific embodiments. However, it is not used as any restrictive basis for the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative operations belong to the scope of protection of the present invention.

[0086] An optimized control method for a motor applied to a single-degree-of-freedom direct-drive wave energy generation system provided by the present invention includes the following steps:

[0087] S1. Establishment of the mathematical model of the permanent magnet linear generator

[0088] S2. Establishment of the mathematical model of the maximum wave energy capture condition

[0089] S3. Parameter setting and optimized control experimental method of the permanent magnet linear generator

[0090] Further, according to Figure 1 , the establishment of the mathematical model of the permanent magnet linear generator includes the following steps:

[0091] The permanent magnet synchronous linear motor (PMSLG) can be modeled mathematically by imitating the permanent magnet synchronous motor (PMSG). The stator windings are symmetrically distributed in three phases, and the axes of each winding differ by 120° electrical angle; the air-gap magnetomotive force and magnetic flux density generated are sinusoidally distributed; the influence of ventilation grooves and winding slots is ignored, and it is assumed that the stator and rotor surfaces are smooth; the influence of magnetic circuit saturation, hysteresis loss, and eddy current loss is ignored.

[0092] Perform a park transformation to transform the electromagnetic quantities represented in the stationary three-phase coordinate system a, b, c into electromagnetic quantities represented in the two-phase rectangular coordinate system d, q rotating with the rotor and the stationary 0-axis coordinate system (collectively referred to as the dq0 coordinate system). The coordinate transformation does not change the internal electromagnetic relationship of the generator.

[0093] The park transformation changes the variable coefficient differential equation into a constant coefficient differential equation. The park transformation with equal power is adopted, and the function is:

[0094]

[0095] In the three-phase stationary coordinate system, the voltage function of the three-phase circuit of the PMSG stator is:

[0096]

[0097] In the formula, R a , R b , R c are the three-phase resistances. Also, because the three-phase windings are symmetric, so R a = R b = R c = R s ; i a , i b , i c are the three-phase stator currents; φ a , φ b , φ c are the three-phase stator magnetic fluxes, and the corresponding magnetic flux functions are:

[0098]

[0099] In the formula, L is the self-inductance and are all equal; M is the mutual inductance and are all equal; φ f is the permanent magnet magnetic flux; θ is the angle between the d-axis and the a-axis, θ = ω e t; ω e is the electrical angular velocity, n p$p$ is the number of pole pairs of the motor, and $\tau$ is the pole pitch of the motor. After the equal-power Park transformation, the voltage functions in the dq-axis rotating coordinate system are:

[0100]

[0101] $u$ d 、$u$ q 、$i$ d 、$i$ q are the stator voltages and currents on the dq axes respectively; $L$ d 、$L$ q are the equivalent inductances on the dq axes respectively, and $L$ d =$L$ q =$L$ s ; $\varPsi$ d 、$\varPsi$ q are the equivalent fluxes of the stator flux linkage on the dq axes. The equivalent flux function is:

[0102]

[0103] From the above formulas, the complete expressions of the voltage functions of the permanent magnet synchronous generator on the d and q coordinate axes are obtained:

[0104]

[0105] Through the above formulas, the SVPWM control of the generator based on $i$ d =0 can be realized.

[0106] The electromagnetic force $F$ pto of the generator can be obtained by analogy with the electromagnetic force of the motor, and its functional form is:

[0107]

[0108] Also, because $i$ d =0, $L$ d =$L$ q =$L$ s , the simplified function is:

[0109]

[0110] The induced electromotive force $E$ of the PTO device is:

[0111]

[0112] The stator voltage $u$ is the voltage difference between the output voltage $U$ and the induced electromotive force $E$ of the PTO device, which is:

[0113]

[0114] Furthermore, the establishment of the mathematical model of the maximum wave energy capture condition includes the following steps:

[0115] Float dynamics function:

[0116] Z b is the displacement of the float body relative to the hydrological zero point; is the acceleration of the float body

[0117] M b is the total mass of the float body and the mover of the linear generator

[0118] F e is the wave force

[0119] F hs is the hydrostatic restoring force: F hs =-K hs ·Z b

[0120] K hs is the equivalent elastic coefficient of seawater, which is related to the geometric structure of the float body

[0121] F pto is the thrust of the PTO device, that is, the electromagnetic thrust of the linear motor

[0122] F rad is the radiation force on the float body

[0123] Based on the study of wave forces, under irregular waves, the convolution integral formula of the Cummins equation is introduced to describe the fluid memory effect, and the corresponding radiation force function:

[0124]

[0125] After organizing the above formulas, the dynamic equation of the single-degree-of-freedom direct-drive wave power generation device can be obtained:

[0126]

[0127] Furthermore, the frequency-domain equation of the direct-drive wave power generation system is obtained:

[0128]

[0129] In the formula, F g is the counter-electromagnetic force, which is the interaction force of the electromagnetic thrust F pto ; B0 is the radiation force damping coefficient, and from the above formula, we can get:

[0130]

[0131] When the counter-electromagnetic force of the direct-drive wave energy generation system is only linearly related to the float body velocity, it can be expressed as:

[0132]

[0133] Wherein R e is the optimal damping coefficient of the direct-drive wave energy power generation system.

[0134] The velocity difference angle θ and R between the wave and the float body e and ω can be respectively expressed as:

[0135]

[0136] After Laplace transform, it can be obtained:

[0137]

[0138] When the damping Z of the energy output system e is equal to the conjugate of the internal impedance Z1 of the wave energy conversion system, the maximum wave energy capture condition can be obtained:

[0139]

[0140] The optimal velocity of the float body is obtained as:

[0141]

[0142] The system dynamics model can be equivalent to a second-order resonant circuit, and the response form of the system can be compared to series resonance.

[0143] Under the condition that the device realizes the maximum wave energy capture, as long as the motion stroke, acting force, and output power of the permanent magnet linear generator of the wave energy power generation device are within the allowable range, resonance can be achieved in any wave energy environment, so that the device can capture the maximum wave energy, and its application area is wide. In the operation of the PMLG, energy often undergoes bidirectional transfer. When the energy flows forward, the motor outputs electrical energy as a generator, and vice versa, electrical energy is input as a motor to input energy to the PTO.

[0144] Furthermore, according to Figure 2 , the parameter setting of the permanent magnet linear generator includes the following steps:

[0145] Furthermore, for the selection of the primary and secondary structure, although the long secondary structure uses more permanent magnet materials, the entire stator winding is an effective winding, and the energy conversion efficiency is high. From the perspective of high-efficiency energy conversion, the long secondary structure is selected for research in this paper.

[0146] Furthermore, for the parameter selection, the float body of the direct-drive PTO device is connected to the mover of the linear motor through a connecting rod. Driven by the wave force, the float body moves to drive the mover of the linear motor to perform vertical heaving motion. Under ideal conditions, the motion equation of the wave can be described as:

[0147]

[0148] Let \(H\) be the wave height and \(\lambda\) be the wavelength. When the sea wave level is 4, \(H = 2.5m\) and \(\lambda = 30m\). Under ideal conditions (ignoring factors such as motor friction and wave reflection, \(\varphi = 0\)), the motion velocity equation of the wave can be expressed as:

[0149] \(v = 0.26\sin(0.21t)\)

[0150] From the above equation, the maximum motion velocity of the wave is \(0.26m / s\). For the convenience of data processing without losing the verification of the motor performance, a constant velocity of \(0.26m / s\) is given to the mover, and an optimal control experiment analysis is carried out on the linear generator.

[0151] Furthermore, the optimal control experiment analysis process of the permanent magnet linear generator includes the following steps:

[0152] The permanent magnet linear motor has 9 poles and 12 slots, \(m = 3\). The modeled linear generator is the same as the long secondary model. Since the linear generator model is completely symmetric left and right, for the convenience of analysis, only the right side is modeled here. The designed motor is a three-phase permanent magnet linear motor, and the label groups of the windings of phases A, B, and C are set

[0153] According to Figure 3 、 Figure 4 , the presence or absence of the auxiliary slot structure makes a great difference in the flux distribution at the stator end. The auxiliary slot can convert a part of the leakage flux into effective flux, greatly reducing the change rate of the air-gap magnetic resistance, and theoretically reducing the detent force on the mover. To reduce the detent force on the mover, the stator structure described above is improved, and the end teeth and slots are widened, which is equivalent to the function of an auxiliary slot.

[0154] According to Figure 5 , when the mover of the motor with the auxiliary slot moves, the detent driving force it receives is below 70N and fluctuates frequently around 0 except for a few places with larger amplitudes. It is about 30N less than the detent driving force of the motor without the auxiliary slot, which proves the correctness of the above theoretical analysis.

[0155] According to Figure 6 , compared with before the motor improvement, the amplitude of the no-load induced electromotive force of the linear motor without the auxiliary slot has increased; the difference between the induced electromotive forces of phase C and phases A and B has decreased. It is proved that after adding the auxiliary slot, the electromechanical energy conversion efficiency of the linear motor is enhanced under the same conditions, and the working efficiency and performance of the motor have been improved, verifying the correctness and rationality of the improvement of the stator tooth and slot structure of the linear motor.

[0156] According to Figure 7, when the linear motor is loaded, the load-induced electromotive forces of the three phases are different from each other and are smaller than those in the no-load case. This is jointly caused by the inherent longitudinal end effect of the linear motor and the armature reaction under load conditions. Moreover, compared with the no-load induced electromotive force, the phase of each phase is shifted. This is because the phase of the no-load induced electromotive force is only determined by the magnetic field generated by the permanent magnet, while under load, it is determined by the combined action of the permanent magnet and the armature reaction magnetic field.

[0157] According to Figure 8 , Figure 9 , in this test, the initial movement direction of the mover is downward. At time 0, the mover of the linear motor is at the highest position, and then the mover starts to move downward with an increasing speed. At 0.5 s, the speed of the mover reaches the maximum of 0.26 m / s. At this time, the no-load induced electromotive force generated by the stator winding also reaches the maximum. After that, the mover continues to move downward, but the speed gradually decreases, and the amplitude of the induced electromotive force also gradually decreases. When the mover reaches the lowest point at 1 s, the speed of the mover is 0, and the induced electromotive force is also 0. Subsequently, the mover moves upward following the wave, and the changes in its induced electromotive force and speed are similar to those when the mover moves downward.

[0158] In summary, for the linear motor with improved stator teeth and slots, the mover will be subjected to a smaller positioning force during movement. Under no-load and load conditions, the three-phase windings of the linear motor mover can generate induced electromotive forces at a constant speed and a sinusoidal speed, and the changes in the amplitude and phase of the induced electromotive force are reasonable, which proves the correctness and rationality of the structural design of this linear motor and can further achieve high-efficiency conversion of wave energy into electrical energy.

Claims

1. A method for optimizing the control of a permanent magnet linear generator applied to a single degree of freedom direct-drive wave energy generation system, characterized in that: The following steps are involved: S1. Establishment of mathematical model of permanent magnet linear generator; S2. Establishment of mathematical model for maximum wave energy capture conditions; S3, permanent magnet linear generator parameter setting and optimization control method; in step S1, the stator winding is three-phase symmetrically distributed, and the axes of each winding differ by 120° electrical angle; the generated air gap magnetomotive force and magnetic flux density are sinusoidal distribution; the influence of ventilation grooves and winding slots is ignored, and it is assumed that the stator and rotor surfaces are smooth; the influence of magnetic circuit saturation, hysteresis loss and eddy current loss is ignored; Park transformation is performed to transform the electromagnetic quantities represented by the stationary three-phase coordinate system a, b, c into the electromagnetic quantities represented by the two-phase rectangular coordinate system d, q rotating with the rotor and the stationary 0-axis coordinate system; the coordinate transformation does not change the electromagnetic relationship inside the generator; Park transformation transforms the variable coefficient differential equation into a constant coefficient differential equation. Using equal power Park transformation, the function is: In the three-phase stationary coordinate system, the PMSG stator three-phase circuit voltage function is: Where R a , R b , R c is the three-phase resistance, and because the three-phase winding is symmetrical, R a =R b =R c =R s ;i a 、i b 、i c is the stator three-phase current; φ a ,φ b ,φ c is the three-phase stator flux, and the corresponding flux function is: Where L is the self-inductance and they are all equal; M is the mutual inductance and they are all equal; φ f is the permanent magnet flux; θ is the angle between the d-axis and the a-axis, θ=ω e t;ω e is the electrical angular velocity, n p is the number of motor pole pairs, τ is the motor pole pitch; after equal power park transformation, the voltage function in the dq axis rotating coordinate system is: u d 、u q 、i d 、i q are the dq axis stator voltage and current respectively; L d , L q are the equivalent inductances of the dq axes, L d =L q =L s ; φ d ,φ q is the equivalent flux of the stator flux under the dq axis, and the equivalent flux function is: From the above formula, the complete expression of the voltage function of the permanent magnet synchronous generator under the d and q coordinate axes can be obtained as follows: The above formula can be used to realize the generator based on i d = 0 SVPWM control; Generator electromagnetic force F pto Analogously to the electromagnetic force under the motor, its function form is: Because I d =0,L d =L q =L s , the simplified function is: The induced electromotive force E of the PTO device is: The stator voltage u is the output voltage, and the voltage difference between U and the induced electromotive force E of the PTO device is:

2. The method for optimizing control of a permanent magnet linear generator for a single degree of freedom direct-drive wave energy generation system according to claim 1, characterized in that: The step S2, establishing a mathematical model of the maximum wave energy capture condition, comprises the following steps: Float dynamics function: Z b is the displacement of the float body relative to the hydrological zero point; is the acceleration of the float; M b is the total mass of the float body and the linear generator rotor; F e is the wave force; F hs Still water recovery: F hs =-K hs ·Z b K hs is the equivalent elastic coefficient of seawater, which is related to the geometric structure of the float body; F pto is the thrust of the PTO device, i.e. the electromagnetic thrust of the linear motor; F rad is the radiation force on the float; According to the study of wave force, under irregular waves, the convolution integral formula of Cummins equation is introduced to describe the fluid memory effect, and the corresponding radiation force function is: After sorting out the above formulas, the dynamic equation of the single-degree-of-freedom direct-drive wave power generation device can be obtained: Furthermore, the frequency domain equation of the direct-drive wave power generation system is obtained: Where: F g is the counter-electromagnetic force, is the electromagnetic thrust F pto interaction force; B0 is the radiation force damping coefficient, from the above formula we can get: When the anti-electromagnetic force of the direct-drive wave energy generation system is only linearly related to the speed of the float, it can be expressed as: Where R e The optimal damping coefficient for the direct-drive wave energy generation system; The speed difference between the wave and the float is angle θ, R e , ω can be expressed as: After Laplace transformation, we can get: When the damping Z of the energy output system e When it is equal to the conjugate of the impedance Z1 in the wave energy conversion system, the maximum wave energy capture condition is obtained: The optimal speed of the float body is obtained as: The system dynamics model can be equivalent to a second-order resonant circuit, and the system response can be compared to series resonance; Under the condition that the device can achieve maximum wave energy capture, as long as the movement stroke, force and output power of the permanent magnet linear generator of the wave energy power generation device are within the allowable range, resonance can be achieved in any wave energy environment so that the device can capture the maximum wave energy. It has a wide range of applications. During work, PMLG often transfers energy in both directions. When the energy flows forward, the motor outputs electrical energy as a generator, and vice versa, it inputs electrical energy as a motor to input energy to the PTO.

3. The method for optimizing control of a permanent magnet linear generator applied to a single degree of freedom direct-drive wave energy power generation system according to claim 2, characterized in that: The following steps are involved: The primary pole structure is selected. The permanent magnet of the long secondary structure is longer than the stator winding. Although more permanent magnet materials are used, the entire stator winding is an effective winding, and the energy conversion efficiency is high. From the perspective of efficient energy conversion, this paper selects the long secondary structure for research; Parameters are selected, the float of the direct-drive PTO device is connected to the mover of the linear motor through a connecting rod. Driven by the wave force, the movement of the float drives the mover of the linear motor to swing up and down; under ideal conditions, the wave motion equation is described as: H is the wave height, λ is the wavelength; when the wave level is level 4, H = 2.5m, λ = 30m. Under ideal conditions, the wave motion velocity equation is expressed as: v=0.26sin 0.21t From the above formula, we can get the maximum wave speed of 0.26m / s. In order to process data conveniently and verify the motor performance, a constant speed of 0.26m / s is given to the mover, and the linear generator is optimized and controlled experimentally analyzed. The permanent magnet linear motor has 9 poles and 12 slots, m=3. The modeled linear generator is the same as the long secondary model. Since the linear generator model is completely symmetrical on the left and right, for the convenience of analysis, only the right side is modeled. The motor is designed as a three-phase permanent magnet linear motor, and the number groups of the three-phase windings A, B, and C are set. The auxiliary slot structure is optimized. The presence or absence of the auxiliary slot structure makes a big difference in the magnetic flux distribution at the stator end. The auxiliary slot can convert part of the leakage magnetic flux into effective magnetic flux, greatly reducing the rate of change of the air gap magnetic resistance. In theory, it can reduce the positioning force on the mover. In order to reduce the positioning force on the mover, the above stator structure is improved and the tooth slot at the end is widened, which is equivalent to the role of an auxiliary slot. Compared with the motor before improvement, the no-load induced electromotive force amplitude of the linear motor without auxiliary slots has increased; the difference between the induced electromotive force of phase C and phases A and B has decreased; it is proved that after adding auxiliary slots, the electromechanical energy conversion efficiency of the linear motor is enhanced under the same conditions, and the working efficiency and performance of the motor are improved, which verifies the correctness and rationality of the improvement of the stator slot structure of the linear motor; When the linear motor is loaded, the load induced electromotive force of the three phases is different and smaller than that when it is unloaded. This is caused by the inherent longitudinal end effect of the linear motor and the armature reaction under load. Compared with the unloaded induced electromotive force, the phase of each phase is offset. This is because the phase of the unloaded induced electromotive force is only determined by the magnetic field generated by the permanent magnet, while when it is loaded, it is determined by the magnetic field of the permanent magnet and the armature reaction. The initial movement direction of the test mover is downward. At time 0, the mover of the linear motor is at the highest position. Then the mover starts to move downward, and the speed becomes faster and faster. At 0.5s, the mover speed reaches a maximum of 0.26m / s. At this time, the no-load induced electromotive force generated by the stator winding also reaches a maximum. After that, the mover continues to move downward, and the speed gradually decreases, and the amplitude of the induced electromotive force also gradually decreases. When the mover moves to the lowest point at 1s, the mover speed is 0, and the induced electromotive force is also 0. Subsequently, the mover moves upward following the wave, and its induced electromotive force and speed changes are similar to those when the mover moves downward. After the stator slots of the linear motor are improved, the rotor will be subjected to smaller positioning force when moving. Under no-load and load conditions, the three-phase windings of the linear motor rotor can generate induced electromotive force at constant speed and sinusoidal speed, and the amplitude and phase changes of the induced electromotive force are in line with common sense, which shows that the structural design and control method of this linear motor are correct and reasonable, and can further realize the efficient conversion of wave energy into electrical energy.

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